Can I say "会社をやめたかもしれません。"? Is the second usage acceptable in Japanese?
Assuming "I" as the subject, The latter sentence, 会社をやめたかもしれません, means "I may have quit my company." simply because やめた is the ta-form (past tense) of やめる. Such a sentence is uncommon, but can be used:
If you are talking about what you will do in the future, 会社をやめたかもしれません never works. You always have to say 会社をやめるかもしれません.
The second sentence is grammatically correct. When you ask "does it make sense", you are asking if it is semantically feasible.
The first is
Grammatically: (subject) might quit the company.
Semantically: (subject) could be first or third person.
The second is
Grammatically: (subject) might have quit the company.
Semantically: Normally, (subject) could only be third person, because if it were first person, that person would know beyond doubt. Although, at a stretch, there could be exceptional circumstances under which even first person did not know whether they had quit or not.