There is a new chapter entitled “Pushouts of Algebraic Spaces”. Here is a link to the introduction. It contains a section on something that is often called formal glueing of quasi-coherent modules. The name presumably comes from the fact that this can be used and is often used to glue coherent sheaves on Noetherian schemes given on an open and on the formal completion along the closed. However, the mathematics is more like what one does when studying elementary distinguished squares in the Nishnevich topology — in fact, I wonder what topology we get if we replace elementary distinguished squares by the notion in Situation Tag 0AEV? Hmm…