Do you have symptoms?
My response would be if I still have symptoms that:
1) The thyroid gland naturally produces not just T4, which is what is in the Synthroid you are likely on, but T3, T2, T1, and calcitonin.
2) The major part of those things are T4 (around 90%) and T3 (around 10%). You aren't supplementing and replacing what the thyroid makes if you supplement with only T4. The T3 is required to help the cells get energy to convert the T4.
3) There are numerous medical references that state that adding T3 can be very effective to help.
4) Most doctors that are patient-centric and not medical establishment centric observe that patients feel their best when T3 is near or above the maximum range.
If you're stable and don't have any hyperthyroid problems, the addition of some Armour or Cytomel may help you out lots.