Quite different meanings:
a) non posso fare XYZ
I cannot do XYZ (I am not capable of, I don't have permission to)
b) non ne posso piu` di XYZ
I cannot stand anymore XYZ
/ne/ is quite a difficult multiple-use particle, in this case it is necessary, but for now
I think it is better that you see (b) as an idiomatic expression, as it actually is.
c) non posso piu` sopportare XYZ
same meaning as (b), but not in idiomatic form.
Usually we use /b/, unless the context is very, very formal.