Most payroll software packages can cope with more than one payroll and more than one PAYE authority (reference). In fact, your payroll provider is already likely to be using this functionality because they more than likely have more than one customer.
As for using the same PAYE reference, I'm not so sure you can keep the same reference as this was allocated by HMRC to the company yours took over. However, as I said, I am unsure on this and only HMRC can really tell you. In my experience, even if the payrolls of taken-over companies have often been kept separate, HMRC have insisted upon a change of PAYE reference - usually in order to consolidate both 'companies' to a single tax office.
As for other aspects of transferring employees, I'll defer to wiser heads than mine when it comes to the intricacies of TUPE.