MapJam will be shutting down its services on February 6th, 2017.
If you join MapJam as a member then you can make your own maps and share them or show them on a website, just like Google Maps or MapHub. There are currently only two base maps (OSM and ESRI satellite view).
You can also sign up as a developer and create very tailored maps. The first 100,000 views per month are free which should be plenty enough for a One-Place Study.
They say that as developers we are "able to customize everything ( it’s Open Source), and MapJam is committed to collaborative, open data mapping communities, and our goal is to make time, service, and code contributions to help accelerate the democratization of information."
I have yet to explore it in any detail.
The article on How MapJam Is Building A Scalable Custom Maps Service by a co-founder at MapJam gives a useful summary of what they are trying to achieve.