It doesn't have to be for an existing missile, but it's a lot easier to reuse a similar missile body.
Eg. The JL-1 and JL-2 are naval variants of land based missiles.
Considering the original question asked about universal VLS in general, we know what the dimensions of the Chinese universal VLS are, I think we can safely exclude any pre-existing SRBMs they have in service could be adapted for it.
I think you were speaking along the right lines -- i.e.: a new, larger diameter universal VLS allows for benefits of firing larger diameter munitions.
However obviously even the smallest Chinese SRBMs are too large for the universal VLS. However the Chinese universal VLS is still much larger than Mk-41 and even Mk-57 when using the cold launch configuration (enabling use of the full 0.85m diameter), that will enable larger munitions in future as they are developed.