I like the text. I second Wolfgang in regards to the upper case comment. Plethora might also be an alternative to multitude though some people might understand it in a pejorative sense.
I would also favour a few minor language edits (cf. in bold):
TransforMap will provide/provides an online-platform for you You to visualize the myriads/ multitude of alternatives to the dominant economic model on a single, multilayered map. It will give to [unnecessary, should be erased imo] everybody the opportunity to map all the initiatives, communities, projects, worker-owned, self-managed or (at least) democratically organised companies and other institutions dedicated to meeting people's needs, serving the common good and/or contributing to a sustainable way of life.
TransforMap will show all the 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.
TransforMap invites all the existing mapping initiatives to cooperate for creating an open map based on a common taxonomy, Free Software and standardised APIs. It will be/is published under an Open Data License.
Our world is transforming. There are old and new alternatives all over the planet. TransforMap will show you how to get there. [TransforMap shows where to find them ?]
[Join the map, join the movement! ?]