The biggest issue with using conductors in parallel is overheating. Code gives explicit permission for conductors in parallel, with limitations to prevent overheating.
When conductors are in parallel, the current will divide between the conductors in inverse proportional to the impedance of the individual conductors. Thus code requires conductors to have the same characteristics (same material, same conduit material, same length, etc.)
Code also specifies a minimum allowed conductor size for conductors in parallel, my _guess_ is that this is to ensure that normal manufacturing and installation tolerances (no two conductors can have the _exact_ same characteristics) do not have a material impact on the 'same characteristics' requirement.
Code specifies a minimum allowed EGC size. Multicore cables generally have an EGC sized for the conductors used individually; it is very likely that the EGC will be too small if conductors are used in parallel for increased ampacity.
Under NEC code, conductors in parallel used per the requirements above may be used at their full ampacity. This might be part of the reason that the NEC code is so strict about making sure the current divides evenly. I recall at least one non-NEC situation where smaller conductors were permitted in parallel, but the parallel sets could not be used at full ampacity (eg. 3 conductors in parallel at 2.25x the ampacity of a single conductor).
-Jon