[1]:https://mathoverflow.net/questions/40945/compelling-evidence-that-two-basepoints-are-better-than-one


Grothendieck in his 1984 "Esquisse d'un programme" (Section 2) wrote (English translation):

" ..,people still obstinately persist,  when calculating with fundamental groups, in fixing a single base point, instead of cleverly choosing a whole packet of points which is invariant under  the symmetries of the situation, which thus get lost on the way.  In certain situations (such as descent theorems for fundamental groups \`a la van  Kampen) it is much more elegant,  even indispensable for understanding  something, to work with fundamental groupoids with respect to a suitable    packet of base points,.."

Question: Does anyone have any reference to relevant work on "descent theorems for fundamental groups"? 

Relevant to this question is this mathoverflow  [discussion on several base points][1].