The principle problem I can see with doing that in this instance is that the gap between the trimmer and the masonry wall is very narrow - in fact it looks too narrow to get a drill in there to make perpendicular holes in the masonry (in order to fix a ledger). As to chopping out pockets in the masonry (to take joist ends) or even hammering twist nails into joist hangers you'd ideally need to use on the trimmer - both are going to be difficult. I'd be a bit wary about putting in another joist paralle to the existing trimmer, but I suppose that could be OK gioven that the length isn't too long.
However, another photo shows joist ends minus trimmers:
which would surely indicate that short sistered joists, bolted together with at least a 1m overlay would do the job, wouldn't it?