One detail that seems quite common to conlangs that I guess is justifiedly common is a detail in verb morphology. It seems both nature and conlangers like verbs to mark person -wals.info gives 83 languages without any person marking on their verbs in its sample, and about 300 with. Granted, of those 300, less than those without person marking exclusively have exclusively subject-marking. Conversely, about 200 mark both subject and object, 24 mark only the object, and six have a system where either the subject or the object is marked.
Anyways, we could maybe try and do something else. Maintain marking with roughly the same amount of different markings, but having some entirely different things instead of person.
Here's one suggestion, and I hope others can come up with other ideas that deviate in other ways:
present transitive, non-past intransitive, non-past existential, present intensive transitive, present intensive non-transitive (includes existential)
past transitive, past intransitive (merges with past existential), past intensive (merges all)
future transitive, future intensive (merges all)
note: negative and intensive do not combine at all; an auxiliary can be turned intensive, though, and have a negative complement.