There's no limit on points, but there is a few limits on map functionality. As you say - dual-axis, so one axis can be polygons and the other axis can be points, but you can't do more than that.
Depending on what you're trying to achieve, you could change the polygons displayed using filters &/or calculated fields.
What specifically are you trying to achieve?
Tableau has some preloaded data layers from public sources like the ACS and Census. You can add as many of those as you want.
As far as loading in your own data layers from wherever and having the ability to toggle them on and off like in arcmap or qgis, no, tableau doesn't have that functionality right now.
There used to be a way to do it with Mapbox Classic, but no longer.