MPLS aka PWAN is ideal for linking high numbers of sites on a private network. This is usually configured as hub & spoke with the hub at your data centre but it can be configured as a mesh network. At no point does the traffic traverse the Internet although it is possible to breakout at an Internet Gateway if this is a requirement.
A typical configuration would be for 5 or more sites with an Ethernet circuit at the central site and DSL tails into the remote locations. This can include staff working from home. The overall network will be designed to meet your current and future business needs and can include QOS to prioritise traffic such as VOIP.