We analyze the extension of the Minimal Supersymmetric Standard Model which includes extra Y=(0,\pm 1) supersymmetric triplets with a global SU(2)_L \otimes SU(2)_R symmetry spontaneousy broken to the custodial SU(2)_V by the vacuum expectation value of the neutral scalar components of doublets and triplets. The model is the supersymmetrization of the non-supersymmetric model introduced long ago by Georgi and Machacek where the ��-parameter is kept to unity at the tree-level by the custodial symmetry. Accordingly the scalar sector is classified into degenerate SU(2)_V multiplets: singlets, triplets (including the one containing the Godstone bosons) and fiveplets. The singly and doubly charged chiral superfields play a key role in the unitarization of the theory. The couplings of the Standard Model-like Higgs to vector bosons (including ����) and fermions, and the corresponding Higgs signal strengths, are in agreement with LHC experimental data for a large region of the parameter space. Breaking of custodial invariance by radiative corrections suggests a low-scale mechanism of supersymmetry breaking.

33 pages, 9 figures. v2: Version to appear in PRD. Typos corrected and references added. Figs. 9 and 10 improved