I think that the best way to handle this is to essentially give them slightly fewer mutation points than a pure zerg would have, since they already have arms and legs (I would tentatively say identical to the zerg racial class, but a flat reduction of 1 or 2 mutation points). Another option would be to drop quick mutations, since they can't change their body quite as easily. Or perhaps just prevent them from dropping the limbs that they have from their other race when performing a quick mutation or when gaining a class level, but let them modify their limbs as normal by adding hooves, claws, or whatever else they want that they qualify for. Do whatever you think is best.
As for extra attacks (with extra limbs, for example), those are done via the Multiweapon Fighting feat, as explained in the Mutation class feature, because I feel like it's just easier to deal with than that complicated natural attack stuff described in the Monster Manual. The basic idea is that zerg natural weapons are treated like manufactured weapons for the purposes of multiple attacks, feats, etc. and therefore benefit from Multiweapon Fighting (the monster version of Two Weapon Fighting) rather than Multiattack. Remember to tell the player to keep their Dexterity up so they can take that series of feats if they want some bonus attacks. There's nothing wrong with getting more limbs, but I would also drop the max limbs mutation from 2 + 1 per 4 class levels to just 1 per 4 class levels, since the character already has two pairs of limbs (presumably). Other than that, feel free to hand them everything that the zerg racial class offers.
Make sure there's a good in-game explanation for why this character suddenly has zerg powers though. Did they get hit by a weakened version of a zerg virus or something?