According to Glen Brown, “One of the greatest things about Andorra is that the country is outside the EU and this is why you get duty free. This means when you need to do your 90 days out of the Schengen zone you can do those 90 days in Andorra if you wanted to and then slip back into the Schengen zone for another 90 days again.”
I am suspicious that there is some detail that Mr. Brown has overlooked. I read elsewhere that Andorra had agreements with both Spain and France to not let in anyone who isn’t legally authorized to be in those countries. I’ve also read a claim that Andorra allows a tourist 183 days and another saying it is only ninety. An actual residence permit has a set of financial requirements much higher than that of Spain.
Would it actually be legal to alternate between Andorra and France or Spain?
If Andorra limits one to ninety days, and measures it the same way Schengen does, then I think it wouldn’t work, because the day you cross the border counts for both.
Related: https://en.wikipedia.org/wiki/Talk:Schengen_Area#How_many_micro_states?