We can sponsor H-1B transfers, TN visas for Canada/Mexico citizens (we did this for Render's first engineer), H-1B1 visas for Singapore citizens, and pretty much any other work visa that's not a new H-1B. If you're on an OPT, we will file a new H-1B for you because you're already here.

We will eventually grow out of this constraint, but it's personally frustrating because my own first job out of college was on an H-1B visa.