MPLS question. Two phisycal links between directly connected LSRs.

Hi, everyone!

There is MPLS Backbone with full-mesh RSVP LSPs between 4 routers(R1 - R4). Please, see the picture below. I've added new phisycal link between R3 and R4(RED curved line). My question: is it possible to include this link into MPLS BB as separate LSP? My goal is to direct specific traffic only in this new LSP and don't let another traffic to go through this. And more general question: is it even possible to have two separate LDP/RSVP sessions between two directly connected(via Ethernet) LSRs?

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network diagram pic:

https://ibb.co/zfDWL2C