No sensible buyer (i.e. not strategic) is going to pay high revenue multiples for a private illiquid company. Exceptions to this might be when they have some advantage (existing customers etc) to sell to. But nearly all PE shops overpay on large deals.
By strategic, I don’t mean “sensible” or “smart”, I mean it’s a buyer where the asset is considered strategic, hence it would always fit under your “when they have some advantage” umbrella.