Is it possible to insert DNA without cutting the recognition site with CRISPR/Cas9?
Look into site-specific recombination.  You can use a site-specific recombinase, specifically an integrase, that can insert a sequence of DNA at a certain attachment site.  You can add an identical attachment site into the DNA sequence to insert, allowing for the reintegration of a new attachment site.  Note however that you might get SSR onto the insertion plasmid itself, so don't do this if you need a specific amount of integration.



Look at the bottom subfigure of A for an example of integration.  Recombinases can also do other things, such as excision and inversion, based on the orientation of the attachment sites.