As a pilot in EASA land, intending to work for multiple AOCs, the amount of types you are allowed to fly commercially at the same time is most likely the only regulatory limit out there. The maximum is two.
You can fly with as many operators as you are able to, provided there is no restriction in your contract (which is not a regulatory thing).
OCC is done when joining an operator and is kept current with annual recurrent trainings & checks. (OPC, line check,...). If you stay current in that regard, there is no need for another OCC, unless you are changing type or upgrading to CPT. Even falling out of currency does not necessitate an entire OCC.