Lawyer/alum here to shed light on what President Ono probably meant in his Big Ten letter's reference to conference rules.*

Bottom line: no matter much Michigan's conference rivals whine and pound the table demanding "instant action," Big Ten Commissioner Pettiti doesn't have the authority to instantly suspend Harbaugh or otherwise discipline Michigan for the Conor Stalions ticket-buying scheme (or whatever else the SignGate "scandal" consists of) until the NCAA finishes its investigation.

* (Not-legal-advice, not-licensed-in-Michigan, only-vaguely-familiar-with-the-facts, and not-an-expert-in-sports-law disclaimers apply — this is just a take that is more informed than your average take if I am analyzing the correct rules.)

I. The rules

The relevant Big Ten rules seem to reside in the Big Ten Conference Handbook as amended by the Sportsmanship Policy (2022–23 version available on the B10's website at the link; the policy was originally adopted in 1974). The Sportsmanship Policy replaces Agreement 10 of the Handbook, not the Handbook as a whole.

The Big Ten Conference Handbook — Rule 32 ("Enforcement Policies and Procedures")

The latest online version of the handbook I can find is from 2018–19. For what it's worth, the rules I describe below are alluded to in an ABC News story today by Adam Rittenberg, suggesting that the rules remain in effect today. (I used advanced searches on Google and a legal research database and didn't find any newer versions.)

Rule 32 of the 2018–19 Conference Handbook divides investigations into two groups for purposes of determining the applicable procedure. Each investigation is either (1) initiated by the NCAA ("NCAA Initiated Cases") or (2) initiated by the Big Ten ("Conference Initiated Cases"). See Rule 32.2.2 ("Investigations"). My understanding is that despite some early inaccurate reporting to the contrary, the SignGate investigation originated with the NCAA, not the Big Ten.

In investigations initiated by the NCAA, the Big Ten rules require the conference to wait for the NCAA investigation and any appeals to be finished and for the NCAA to levy a penalty first, at which time the Big Ten can choose to pile on (key language italicized):

32.2.2(C) NCAA Initiated Cases. The Compliance and Reinstatement Subcommittee shall review violations by member universities as determined by the NCAA and may impose penalties in addition to those imposed by the NCAA for any violations.

1. Where the NCAA initiates a preliminary or official inquiry with a member university the Conference will cooperate with university and NCAA representatives in the processing of that case through the normal NCAA investigation, hearing and appeal processes.

2. While the case will be processed through normal NCAA channels, the Conference Compliance and Reinstatement Subcommittee shall review the case and may impose additional penalties, if warranted, subsequent to the NCAA action.

That provision is unambiguous and lists no exceptions. There is no rule in the conference handbook that would allow the Commissioner to bypass the NCAA (and the Big Ten's Compliance and Reinstatement Subcommittee) because the Commissioner feels peer-pressured to act quickly.

The Big Ten Sportsmanship Policy

The Sportsmanship Policy just replaces one set of provisions in the Handbook ("Agreement 10"); it exists alongside the enforcement provisions described above. In fact, Rule 32 in the Handbook (discussed above) begins by noting:

Also See Men's and Women's Agreement 10 for Policies & Procedures on Sportslike Conduct ...

The Sportsmanship Policy is much broader and vaguer in scope than Rule 32. The Sportsmanship Policy's key language describing its scope is as follows; I've replaced unnecessary language with ellipses and added a paragraph break for clarity.

The Big Ten Conference expects all contests involving a member institution to be conducted without compromise to any fundamental element of sportsmanship. Such fundamental elements include integrity of the competition, civility toward all, and respect, particularly toward opponents and officials. Accordingly, each member institution ... has an obligation to behave in a way that does not offend the elements of sportsmanship described above.

Actions that are offensive to the integrity of the competition, actions that offend civility, and actions of disrespect are subject to review and are punishable in accordance with the terms of this policy. Although this policy will apply most commonly to actions that occur within or around the competitive arena, the scope of its application is intentionally left unrestricted in order to accommodate any behavior, which may occur in any setting, deemed by the Commissioner to offend the underlying objective this policy seeks to achieve. For example, public comments or public messaging made at any time ... , including comments or messages posted even temporarily via social media, are subject to review and punishable in accordance with the terms of this policy. ....

The first paragraph above describes the policy's purpose. The second paragraph describes the policy's scope — what it theoretically allows the B10 to punish. The B10 may punish "[a]ctions that are offensive to the integrity of the competition, actions that offend civility, and actions of disrespect." 

That language is so broad as to verge on meaninglessness, so the example provided at the end of the second paragraph is crucial to understanding the policy and reconciling it with Rule 32's enforcement procedures:

For example, public comments or public messaging made at any time ... , including comments or messages posted even temporarily via social media, are subject to review ....

It's within the Commissioner's discretion to find a violation and impose certain penalties on conduct that violates the Sportsmanship Policy. It has been reported that the B10 Commissioner is considering a two-game suspension of Harbaugh; the reason it would be two games and not three is that any longer suspension under the Sportsmanship Policy would require prior approval by the B10 Joint Group Executive Committee (JGEC). Two games, however, would fall under this provision:

10.3.3.1 Standard Disciplinary Action. Standard disciplinary actions shall include admonishment, reprimand, fines that do not exceed $10,000, and suspensions from no more than two contests.

Alas for the haters, Michigan will have a strong legal argument that the Commissioner cannot unilaterally suspend Harbaugh or anyone even for two days for SignGate because the case falls within the "NCAA Initiated Cases" provision in Rule 32 of the Handbook.

II. The Definitive Legal Analysis

Many people seem to think that Big Ten Commissioner Pettiti can act immediately and punish Michigan with at least a two-game Harbaugh suspension on his own say-so because other B10 coaches threw a tantrum and demanded that he DO SOMETHING. This assumes that the Sportsmanship Policy overrides Rule 32 of the Big Ten Conference Handbook. But it doesn't. It only amends the previous Agreement 10 of the Big Ten Conference Handbook, which exists alongside Rule 32.

Assuming the Sportsmanship Policy (Agreement 10) and Rule 32 of the Big Ten Handbook are both in effect, and that their current versions contain the language I've discussed above, the provisions conflict with respect to SignGate and must be reconciled. Michigan wins for three reasons:

1. Based on their language alone, the Handbook and Sportsmanship Policy encompass overlapping conduct. This is inevitably so because of the Sportsmanship Policy's absurd breadth; the policy allows any "actions of disrespect" to be penalized. SignGate consists of Conor Stallions' alleged violations of NCAA rules against in-person scouting, which has triggered an "NCAA Initiated Case" under the Handbook. Assuming SignGate is also an "action of disrespect" or otherwise falls under the Sportsmanship Policy, the Handbook and Policy must be reconciled: must the Handbook's procedures be followed? The answer is yes. If the Big Ten had wanted to amend Rule 32, they would have done so. Instead, they have separate rules on sportsmanship that they've enacted to coexist  with Rule 32. There is no reason to believe that the Policy overrides Rule 32 rather than addressing other situations not encompassed by Rule 32. (The relevant legal-interpretation principles include the "harmonious-reading canon" and perhaps the "presumption against implied repeal"; see Scalia and Garner, Reading Law: The Interpretation of Legal Texts.)
    
2. Since the Policy doesn't override Handbook Rule 32 for situations encompassed by Rule 32, the latter's procedural rules apply to any NCAA investigation — SignGate included. The SignGate investigation is an "NCAA Initiated Case" under Rule 32.2.2(C), and the Big Ten may not take any action to punish Michigan until all three of the following happen: (1) The NCAA investigation and any appeals are concluded; (2) the NCAA levies penalties; and (3) the Big Ten, following the procedures described in Rule 32, determines that additional penalties are warranted. (The relevant legal-interpretation principle is the "General/Specific Canon": specific provisions override general provisions.)
    
3. These conclusions are bolstered by language in the Sportsmanship Policy, which provides only one example of conduct to which it applies: social media messages. Unsportsmanlike social media messages, like other boorish but insignificant conduct (such as Sparty's 2018 field-walking stunt), are plausibly covered by the Sportsmanship Policy but not Rule 32 because they may not violate any particular NCAA or Big Ten rules or trigger any investigations. In such situations, the Commissioner can levy one of the minor penalties described in Sportsmanship Policy 10.3.3.1.

In short, if Pettiti tries to penalize Michigan in any significant way (including by suspending Harbaugh) under the Sportsmanship Policy, Michigan will sue and seek a preliminary injunction blocking the suspension. Another attorney-fan posted about that earlier today. Preliminary injunctions are hard to obtain because of the procedural standard, so a win isn't assured, but Michigan will have the better argument.

Michigan will correctly argue that if the Big Ten Commissioner punishes Michigan in connection with an NCAA-initiated investigation before the NCAA investigation is completed, that violates Rule 32 of the conference rules and is a material breach of the U of M's agreement with the Big Ten. (Note for your arguments on other message boards: although fairness and prudence counsel against the B10 punishing a school before conducting any serious investigation because rival schools pressured them to do so, there's no need to rely on vague values such as fairness or "due process" here since the conference rules solve this question.)

I hope that has been helpful. Go forth to all the social-media venues and message boards you frequent to liberate the masses from their ignorance, one comment at a time. Go Blue!