You could treat it kind of like a router using internal interfaces. Plug the MPLS into LAN2, then LAN 3 is uplink to the rest of that local branch, then setup routes and IPs associated with that LAN2 port in the Addressing and VLANs page. This process is pretty manual for sure. You could then plug the WAN1 port into internet service and let the MX still act as your internet filter and all that good stuff.
IF you have MXs at both / all sides, you could enable their site to site VPN, over the MPLS circuits or over the internet and it can handle routes for you.
I'll say for my experience, we were using an MPLS, but really didn't have a need anything but basic connectivity between sites. After some testing, we ditched MPLS, and each site has a low speed (10-20 mbit) fiber we use as Primary VPN, and a 2nd Coax internet 100 mbit connection we use as Primary internet and fail over VPN as needed. It was a big cost savings for us!
That's a pretty simplistic sum-up, but maybe that will help set you on a good path.