I found pretty much all my work through contracting firms. While employed, I only ever considered offers at current_rate + $25/hr. I noticed after a certain tier of billing rate I got "promoted" from talking to the kind of person that cold calls you asking for a resume to a different tier of salesperson. We're told ego is bad, but ego is a tool. Turn it on when talking to them, and be firm about what you deserve. Once you're off the phone with them you can crank the ego back down to normal so you're not an asshole in daily life.

If you can, find out how much the middle-man company is farming you out for. Let's say you once did a contract through ManPower for ABC company. ABC company needs some labor, and you did a good job, so they reach out to you directly. You should be billing what ManPower billed your time for, not what you billed ManPower.

This is generally only possible to do through smaller businesses. Big corporations typically have contracts where they require you to go through one of their preferred vendors.