Just like title says.
Implement private matches, but implement an intuitive bot system inside it.
Include:
modifiers
Up to 6-8 players
Challenges
Milestones
Ability to restrict loadouts
Reward completed challenges (only for bot system)
If anyone played games like goldeneye and perfect dark then you know what I'm talking about. Having challenges a group can work towards would definitely create an endgame feel and something people replay the hell out of.
Edit: rewards are not based off player vs player. They are directly related to the challenges associated with bot challenges. The only reason private matches are mentioned is because you would implement the bot system in there.
Example:
http://perfectdark.wikia.com/wiki/Combat_Simulator
These don't seem like much, but put in 8 perfect sims and it could take you weeks to beat.
http://m.ign.com/wikis/perfect-dark/Challenges
*Update*
It seems Battlefront 2 is implementing a bot system. The people saying "easier said then done" ... yeah this is to you.
https://www.inquisitr.com/4519862/star-wars-battlefront-2-will-include-an-arcade-mode-where-players-fight-bots-earn-star-cards/
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First off, dear. Private matches should never and will never give you rewards. Secondly, adding an intuitive bit system isn't just a switch to flick. I don't think I know a game that has bots that has mobility like Destiny. I'm sure u fine could do it given time, but you probably won't be that satisfied with the results.