What if...

[Piotr]

you drew a square grid on a Mercator projection (without the land/ocean anymore, just the grid), then shown it on various common projections instead of the standard equidistant grid? I would like Stereographic too (single Stereographic showing more than 1 hemisphere).

[Atarimaster]

you drew a square grid on a Mercator projection (without the land/ocean anymore, just the grid), then shown it on various common projections instead of the standard equidistant grid?

If I understand your question correctly (I’m not sure about that), the result will be unspectacular:
The distance between the horizontal lines is close to »original« (i.e. the square grid you drew on Mercator) at the equator and will be reduced increasingly towards the poles.
The vertical lines of your grid will behave just like a regular graticule.

Regards,
Tobias

[Piotr]

Yes, but how will it look on various map projections? I would like to see this with polar Stereographic.