Adding a strengthening beam under the mast step at ther top of the bulkhead and attached to that bulkhead can be a good idea on a lot of older boats - as I will be doing to my boat. Tritons quite often need this fix as well. But I know of no-one who suggests doubling the whole bulkhead. See the top picture in this link - it enlarges - the boat is a Triton.
Northern Yacht Restoration | 1966 Pearson Triton Circe
Brian