No. Synergy itself supports an unlimited number of companies, so you could easily have two, three, four or even ten thousand businesses or more at absolutely no extra cost. The only limitation is your computer system itself, so for example if you run out of disk space clearly you would not be able to continue.
This contrasts very strongly with competing products like Sage Desktop (minimum £250 to activate an additional company) or Xero (a new contract is required for each additional company but a 15% discount is offered at the time of writing).