So under the old CBA the following applied:
The uniform player's contract stipulates that the player "represents that he does not, directly or indirectly, own stock or have any financial interest in the ownership or earnings of any Major League Club" except under an agreement approved by the commissioner that provides for the immediate sale of that holding should the manager or player move to another club. MLB rules further stipulate that a manager or player who owns a stake in their club shall be ineligible to work for any other club while the commissioner believes that stake is directly or indirectly held by that individual.
That was the old CBA but I think it's been this way forever so I assume it applies now too. But if Ohtani signed a 13 year deal with a no-trade clause then perhaps he could get the commissioner to agree? The other owners would probably cry foul...