Clinical Endocrinology, page 9
On the issue of combining the standard treatment (T4) with T3, the British Thyroid Association's position statement explains that this may be merited in some circumstances:
L-T4 [T4]/L-T3 [T3] combination therapy in patients with hypothyroidism should not be used routinely, as there is insufficient evidence to show that combination therapy is superior to L-T4 [T4] monotherapy…If a decision is made to embark on a trial of L-T4 [T4]/L-T3 [T3] combination therapy in patients who have unambiguously not benefited from L-T4 [T4], then this should be reached following an open and balanced discussion of the uncertain benefits, likely risks of over-replacement and lack of long-term safety data.vOnyebuchi Okosieme, Jackie Gilbert, Prakash Abraham et al. (2015) “Management of primary hypothyroidism: statement by the British Thyroid Association Executive Committee”.