Thank you for posting! Yes, it would be possible to integrate TestRail with multiple issue trackers at the project level, as each individual TestRail project can support a different integration. However, it would only be supported to have one integration per TestRail project at the moment.
You can configure a project level integration under Administration > Projects > (Applicable Project Name) on the Defects/References tabs. Please note any integration you have configured at the project level will override any global integration settings you have configured under Administration > Integration for that particular project.
I hope this helps!