Can I build a startup and work for it, while being on a U.S. L1A visa?

I take this to mean you’re working for a different company than the one you want to startup while on the L-1. Generally there is no visa restriction to start a company. Anyone can file for and incorporate a startup in the US. Where you run into problems is that you can’t actually work for your company in the US unless you have a valid working visa. As some of the other answers point out, you can apply for a few different types of visas depending on the specifics of your situation. Each type has different qualifications and purposes so first you need to decide which visa applies to you.

If you’re interested in forming a business and serving as a passive investor then you should be okay. To be sure, schedule a free initial consult with an attorney at LawTrades. Our legal marketplace has helped many visa holders maneuver through the complexities of immigration law. Hope this helps.