Single LTM with multiple GTM domains

I am currently working on a Datacenter migration and we are re-IP'ing everything and rebuilding all the network appliances. I am working out the BEST, least impactful, way to migrate the GTM appliances to the new DC's. 

Here is the overall situation. Everything is the same version running 15.x.x with a mix of rSeries hardware running VE's and iSeries hardware also running VE's. 

Existing DC's: 
GTM Domain with two GTM's in different DC's

Multiple LTM's all joined to the GTM

New DC's:

Two GTM's in different DC's, blank configuration

Multiple LTM's all joined with the existing DC GTM's

I know that I can add the new GTM's to the existing DC GTM domain, let them sync up, then update the NS records to migrate the DNS flows over to the new DC, but that also sync's over all the technical debt and limits my pre-testing abilities. 

I would like to setup a new GTM Domain in the new DC, build some automation for the WideIP / Pool creation, and manually review / rebuild all the necessary records in the new DC. My hangup is that this is ONLY possible if the LTM appliance can join multiple GTM domains. 

Can a single LTM appliance join multiple GTM domains and report status to multiple appliances? I don't have an easy way to build a test environment and build this out with VE's and validate so I am hoping for some input from the community.