Two different MDMs (two different devices but single Apple ID on both) possible?

I work as a contractor for two different companies, and unfortunately both of them started requiring installation of an MDM profile on my phone. I understand that Apple does not allow multiple MDMs on a single device (regretfully), so I'm contemplating adding my second MDM to another device. Can I do that and still be signed into the same Apple ID on both devices? Since this will likely involve me buying a new phone and keeping my current one for one of the MDMs, I want to be sure it will work. If not, I'll either regretfully switch to Android, which does allow for multiple MDMs on a single device. I need to be able to have both companies' MDMs on two phones with a single Apple ID signed into both.