Do I have to sign a contract for each point of sale?

A contract/amendment should only be signed when a different legal entity is engaged (i.e. a different VAT or RCS number).

Thus, if several points of sale are all associated with the same legal entity (same VAT number), it will only be necessary to sign a single contract.

If, on the other hand, each of your points of sale is registered in the commercial register with a different RCS or VAT number, you will have to sign as many contracts as there are legal entities.