at a stretch/likeliest of all

At a stretch means at once, in one session, without stopping, etc. They would often drive six or seven hours at a stretch.

Likliest of all - the thing most likely to happen. Did you see this in a context that makes it seem like this meaning doesn't work?

At a stretch can also be used to mean 'yes I agree but reluctantly - only if you stretch the meaning/use as far as possible'

For example

Can I use dishclothes as emergency bandages?

Yes, at a stretch (if you have to but it would be best not to).