Reading some of the later reflections and having the wish to include sustainability also in the "dedicated to" segment of the currently second sentence,
my development suggestions:
TransforMap provides an online-platform to map the manyfold alternatives to the dominant economic model. (myriads is not very commons as expression. manyfolds is a suggestion)
TransforMap will visualize all places, spaces and networks that work on fostering cooperation and deepening human relationships through (co-)producing, exchanging, contributing and sharing, for a free, fair and sustainable world.
It gives to everybody the opportunity to map all initiatives, communities, projects, worker-owned, self-managed or (at least) democratically organised companies dedicated to meeting people's needs, serving the common good and/or contributing to a social transformation towards sustainability. (that passage including sustainability transformation seems important to me)
TransforMap provides a single interface to map and publish data from many sources through a unified taxonomy. It is a free and open platform, designed for and by community.
TransforMap invitates all the existing mappings to cooperate for an open solution to map the plenty of alternatives based on a common taxonomy, working with and/or towards Free Software, developing standardised APIs and publishing under an Open Data License.
There are Plenty of Alternatives (TAPAs). TransforMap makes them visible. Our world is transforming, and new alternatives are all over the planet. TransforMap will show you how to get there.
Hope it does not get to long, but I think that is still within the range. Thx for the good drafting and all development work on that short description.