't Hooft showed that Yang Mills theory with spontaneous gauge symmetry breaking Higgs potential is still renormalizable.
Is the Standard Model fully renormalizable?
The potential issues to addressed in your answer are:
Includng the electroweak and strong interaction sectors
The issue of chiral gauge theories.
(previous answer What do we mean when we say 't Hooft proved that Standard Model is renormalizable? does not address the last issue on chiral gauge theories.)