Can You Prevent Restarting Canadian ER Taxes if Corp Tax IDs are Different for Reorganization

The organization is re-organizing and folding/moving the employees under company B into company A soon and both companies have different Corp Tax IDs. The company doesn't want the Employer taxes like EI to restart once the EE moves to the new company. Is there a way for this to be accomplished using parent company in the Corp Tax ID given the Corp Tax IDs are different for Co A vs Co B? Also wondering about how that might complicate other areas like ROEs and T4s. Any insight if it is even possible? Thxs.