Does the private MPLS have internet? Sometimes it makes more sense to setup MPLS on a LAN port and just route 0.0.0.0 to it for the internet. Any internal/VLAN traffic you'd want to route to the next MPLS next hop IP (MPLS Gateway in most cases).
Adam R MS | CISSP, CISM, VCP, MCITP, CCNP, ITILv3, CMNO
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