I think a person's personality can be cloned.
Aside from the ridiculousness of such belief in itself, as already discussed, it would be interesting to figure out what kind of delusions may lead one to want to be obsessed with the very idea of producing clones of a person's character or personality.
Wishing for the power to produce such clones may reflect a need to compensate for a feeling of impotence. Indeed, since the imagined personality clone would somehow reflect or even reproduce the personality of its creator, the delusional wish to produce such clones might reveal a narcissistic, megalomaniac wish for power and dominance.