FICA cap is not per employer. Well, it is from a withholding perspective (only because it would be impractical to make employers monitor withholding outside their control), but once you do your taxes for that year, you’ll get everything you paid in over the cap refunded.

Right, but employers aren't allowed to coordinate to calculate whether the hit the cap together or not. They don't have that discretion. See

https://www.ecfr.gov/current/title-26/part-31#p-31.3121(a)(1...