The meaning of the expression "some other day" is "next time, not now", but what if the expression is used to denote an action which is going to take place in the future, several days in a row? Is it acceptable to use the form days in such a case?
some other day is an idiomatic expression that is only used with a singular day. If you look at instances of some other days, they do not have the idiomatic meaning.
You can use the expression some other time. According to this NGram, it is actually much more widely used than some other day. Note that it is occasionally used about a time in the past, though the context would make this clear.