My team is currently developing legacy product that was bought from another company, and code quality is what you expect when the team had changed several times

My team is currently developing legacy product that was bought from another company, and code quality is what you expect when the team had changed several times already. On one hand, we have immovable deadlines like Steam sales; on the other, bugs in the build immediately impact sales through negative reviews and refunds. So, after seeing so many bugs with our multiplayer, our studio head urged us to spend some time to refactor the damn thing from scratch - while I, the lead developer, has been more cautious about it.