If we are talking about linking branch-office LANs it's doable with VPN hardware/software solutions.
One way to do it is like this:
MAIN: your main site with let's say LAN with 192.168.0.0/24 network
OFFICE-A: your main site with let's say LAN with 192.168.1.0/24 network
OFFICE-B: your main site with let's say LAN with 192.168.2.0/24 network
1. Get two upstream links with publicly accessible IPs
2. Get a setup/hardware to handle routing (and failover) through both upstreams
3. Setup VPN server to allow connections through both links
4. Setup relevant routes to branch offices trough tunnels.
for OFFICE-A and B:
1. Get upstream link and maybe another upstream or 3G provider.
2. Check that it's easy to switch between them (like unplug cable,
plug in another if you don't need automatic failover)
3. Setup VPN client (software/hardware) that can handle multiple
VPN-server targets and handles failover of VPN tunnel.
4. Setup routing so that routing to MAIN goes trough VPN tunnel.
With this setup your terminal service servers have always the same IP and recovery from link failures is relatively fast. Biggest hurdles with this are: witch VPN solution (vendor, software/hardware), does this require network restructuring, in-house expertise or consultant and how to find the needed know-how in your area.
With a setup like this you don't need access to upstream (ISP) routers and you don't need MPLS (if you talking about a big company with big branch offices then MPLS etc solutions are preferable)
If you need publicly available service failover then that's another beast.