Alternatives to "Sketches of an Elephant" Volume 3

As I said in the comment, this would involve a very large number of different references ! (almost one by subsection... )

But to some extend contributors to the nLab already started doing that and it is probably the best place to start if you are interested in material covered by this third volume: https://ncatlab.org/nlab/show/Elephant

On this page you have the announced table of content of Sketches of an elephantn including volume 3, with for most subsection references to page on the nLab covering the idea suggested by the title of the subsection. The nLab page itself will generally not contains enough information to reconstruct the content of the subsection but will surely contains references to other papers and books.

Johnstone's 1977 book 'Topos Theory' is a very good source.