Yes. There are indeed many small, especially regional U.S. VC funds and many funds outside the U.S. that are focused on $50m exits (vs. the Unicorns and Decacorns of huge Silicon Valley VC funds).
Ultimately, though, their financial models are somewhat similar in that their successful investments need to be able to return at least 10x or more, and in aggregate, all the investments need to return > 3x together.
Back into that, and a $2m pre money is high for a lot of these firms until you have significant revenues. $1m is more common if you have some traction already, e.g. raise $350,000 on a $1m pre. And much less if you are pre-traction.
Silicon Valley VC firms often pay much higher prices, but they also expect much, much larger outcomes. The two are closely tied.