I am not interested in read mapping per se.

I am interested in reporting ALL possible end-to-end alignments of a read against a reference that have <= k mismatches (e.g. k = 5). I do not care about the "best" alignment.

Standard DNA & RNA read aligners (bwa, bowtie, STAR, etc.) that try to find the "best" alignment for a read place limits on number of mapping locations for short seeds, or something similar.

Does any read aligner allow FULL sensitivity?

For example, I can use MUMmer3 to report ALL exact matches of a read in a genome (of a given substring length). I am looking for something similar - i.e. full sensitivity - but allowing a limited number of mismatches.

Anybody know of a program that does this? I have been looking but am not convinced of the full sensitivity of the aligners.