Infinite.
I am sure at some point it will matter but after 18 pulls per Credit Karma I still get everything approved including a sub-inflation rate mortgage and an incentive rate car loan.
CK is just TU, I don't know and don't care what the pulls are on the others.
Worst case you take a break for 6-12 months. I don't burn faster than earn, so I could forego for a while.