The answer really depends on your jurisdiction.
You could, via a “Self-Directed IRA” (SDIRA). However, strict rules apply.
UBTI Tax: If the club deal uses debt (leverage), your IRA might owe “Unrelated Business Taxable Income” (UBTI) tax.
Prohibited Transactions: You cannot invest in a deal where you or your family already control the asset. Always check with your tax advisor first.
