The three usual 'basic' tense systems are "past" vs. "non-past", "non-future" vs. "future" and finally "past" vs. "present" vs. "future". Some languages mix these a bit, having different systems in different aspects (e.g. Russian with its present-shaped gap in the perfective aspect - which given the semantics of Russian aspects makes complete sense.)
However, there also exist other tenses beyond these: there are the hodiernal, the hesternal and crastinal tenses, for instance. The names relate to different days: today, yesterday, tomorrow.
Could an unbalanced system exist of, e.g. "hesternal past vs. non-hesternal tenses" or "crastinal future vs. non-crastinal tenses"?
Oh, the weird ideas that pop up while contemplating the tenses of a conlang.