"Our company has a party the day after tomorrow. Can you join?"
You can report this sort of thing. If Duolingo team agrees with you, they can add the alternative correct solution...
In oral speech you can also omit the article "的", so it would be best to mark it correct?
I think 你可以参加吗 should be accepted too. I noticed that a lot of people use 可以 instead of 能 in colloquial speech to ask if someone could make it to an invitation, even though it doesnt express the idea of physical capacity here,