If the support was not part of the original design (as far as you can tell) then a redisign is necessary. Supports must be considered as required by ASME VIII-1 paragraph UG-54.
I remember sitting in a review where the question was asked "....how is this heat exchanger supported?....", the reply was that the support was inherent in the nozzles, and upon further look into the calculations it was determined that the nozzles could not sustain the loads imposed upon them, the solution was to support the vessel with U bolt clamps around the exchanger shell bolted to a rigid support. This information was added to the remarks section of the Data Report as it would help others in the future determine the support requirements.
A thorough check on the history of the vessel should reveal something of value, if not, then a redesign of the support is necessary.
FAQ731-376