I am presuming here that you are referring to E. coli. The answer will be different for different host organisms.
There really is not a limit to how much DNA a vector can hold. Many of the standard cloning plasmids we use have also been adapted to be used as cosmid vectors and carry inserts up to 45kb. The reason you hear about a 10kb limit is that transformation efficiency dramatically decreases as plasmid size increases, so the probability that you will recover very large clones is low (but not zero). Also there are technical hurdles to obtaining high quality DNA larger than 20kb unless you take significant precautions during your DNA preparation.
Cosmids worked because you could package in vitro and infect instead of transforming, this circumvented the transformation problem.
Also people have used BAC clones to carry 50-100kb length inserts for genomic studies.
So it is certainly possible to clone something of 60kb but the limitations are not the plasmid vector.