Anyone with a net worth above $1mm can become a venture capitalist, given that VCs deal with earlier stage companies which, as a result of their youth, are happy to take small checks for minority investments.
Private equity, because it deals with mature companies and (more often than not) involves controlling stakes, requires very, very large checks. And because investors don't like an undiversified portfolio, the PE firm must have the means to write many very, very large checks.
This isn't an undertaking that just anyone can do. Of course, if someone has the means to raise hundreds of millions of dollars, has a nose for investing, is experienced in both buy-side mergers & acquisitions as well as the operations of a company in a given domain, then co-sign your advice.
Though index funds or an advisor would be much less risky for someone with those means.
Are you familiar with what "private equity" is? Note that "private equity" is distinct from "private" "equity."
Private equity is an asset class. equity securities and debt (such as, oh, unpaid medical bills, and the right to collect on them) can be purchased as well as corporations/corporate debt.
Are you sure you understand what I'm saying?
Second, what exactly do you accomplish by doing this, except paying a bunch of money in incorporation fees and drafting documents?
There's a reason why corporate shell games are usually played by people with relatively deep pockets: all the benefits that come from using corporate law require lawyers and accountants, and those are expensive.