Microsoft Hosted Exchange 2010
Do you mean this one? Exchange 2010 SP1 Information for Hosted Service Providers
Exchange 2016 only supported coexist with Exchange 2010 SP3 RU 11 and later. It cannot coexist with Exchange 2010 SP1. So, even if you can create a new machine(you may cannot create new computer in that domain), you still cannot install exchange 2016 to coexist with Exchange 2010 SP1.
In this situation, I would suggest you create a new domain and create Exchange and mailbox in it, then contact your provider to export mailbox data from hosted Exchange server, after that import data to mailbox on your new Exchange server.
By the way, Exchange 2010 reached its end of support on October 13, 2020, I would suggest you try to migrate data for better security.
If the response is helpful, please click "Accept Answer" and upvote it.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.