Lots of shoots from a single point is normal response of elm to hard pruning. They often produce many buds from the exposed cambium around the top of the cut.
Clumps of shoots will quickly thicken the area so I would cut off most of the shoots growing close. Reduce down to 2or 3 that look appropriate. Be careful with new epicormic shoots like these. They are not usually very well attached to the trunk so they can break off at the base if bent or twisted.