It is consistent that the least measurable cardinal can carry exactly one normal measure but in almost all models for this theory there is no supercompact cardinal. It seems existence of a supercompact cadinal forces the least measurable cardinal to have many normal measures. Equivalently this means that the assumption "there exists exactly one normal measure on the least measurable cardinal" is an anti-large cardinal axiom which refutes existence of any large cardinal larger than supercompacts.
Question: Assuming consistency of $\text{ZFC}$ and some suitable large cardinal axiom, is the following consistent?
ZFC + There exists at least one supercompact cardinal +
The least measurable cardinal carries exactly one normal measure