Investment companies usually have a different legal structure than a typical startup and are subject to different regulations. You could however start a conglomerate, like Berkshire Hathaway, that invests in startups like VCs do.

So a "fund" wouldn't legally be allowed to raise money using equity crowdfunding. But a "conglomerate" that invests in startups structured as a C-Corporation could raise money through equity crowdfunding. Hope my reply helps!