Two weeks is all most recruiters have ever offered me, and some did so begrudgingly. Which is weird because if I say yes that actually makes me a worse hire.
Recruiters don’t like people who want >2 weeks because it adds risk that you will renege on the deal, which means they lose out on their payday. But the recruiter isn’t the other party in the negotiation, the hiring manager is.
So don’t negotiate start date until you have an offer and are talking to the hiring manager. Save it to the end and you can say “well, I’m still not 100% sure about this offer, but I think this would work if you could push my start date out a bit…”
Interesting, I was able to get a couple months when I switched jobs a while back. I think recruiters probably figure the longer the window, the more chance you go do something else instead.