Honestly, I think it'd work best in an RPG where party members didn't level up with you. Maybe party members who don't go on a mission with you receive a "Training" XP boost for every mission you complete, but have it be smaller than the smallest sidequest's XP boost for their current level. They don't fall impossibly far behind, but they don't keep up. Have the ability to delegate any quest to any party member at any time, but have a 'delegation limit' as such, where you can only send 1 or 2 party members on each quest, depending on how big and long it is. The others are required for administration or W/E at the camp.
Also, no guarantee of success. The character's class, alongside their level and average equipment level, would be used to determine what happens. If you want more fun, throw in their specialisation too [Is your mage AoE or Single Target Nuke?]. This is checked against what the mission throws at you - say you send your low level single target nuke mage on this Rat Killing Quest, but it turns out there's 20 low level rats, and they gravely wound him before he can complete it because he can't take on that many enemies at once. You should have sent your AoE mage, or tanky warrior, to do the job instead. Meanwhile, if it were one high level rat, you'd want to do the opposite - and if they pass a generic logic check of these things, they succeed at the mission. They receive the experience from it, give you the loot, and will make any necessary decisions among the party while away.
This means that for most of your level missions, you won't want to delegate them, as your weaker party members are likely to fail, and that should come with some penalty. Because of this, you'll personally do most of the important stuff, but the less important things you can send others off to do later, without hard locking it to be this way. All main missions, though, you'd be unable to delegate.
I'd also tie this more into the role playing side, and knowing your party members and getting to know them, rather than a purely mechanical thing. As another poster suggested, your Mushroom Farmer dwarf might make a different choice than your Peta-style conservationist druid when it arises in this rat infestation mission, but I'd take it further than just that. Each character will do their own thing with the mission, and balances a few things. For example, send your kleptomaniac thief on the mission, and he'll steal some of the grain from the cellar. This will worsen your relationship with the farmers of the land, which should be something you want to manage if you're the leader of a large organisation they're no doubt supplying food for. You might send your farmer-dwarf, who asks for less pay from the mission as he understands the troubles that a rat infestation can have on a farm, which will earn you less money, but a greater reputation with the land's farmers. Each character would have a modifier they'd apply to each mission's rewards, based on their personality. This would have to be carefully balanced, so as not to turn this into a min/max exercise, and instead make it a role playing one, but I feel its still a good idea. In fact, if you were clever, a min/max experience could be a role playing experience; if you are the leader of one of these big organisations, you're going to want to make the best choice for your organisation, rather than make it fail, and setting it up so that that is more advantageous, and its less of a Meta choice, would help solve this problem.
As a final layer on this, on missions where multiple party members are completing them, you'd want to know how much they like each other, and talk to them to figure this out. In Dragon Age; Origins, sending Morrigan and Alistair on a mission would result in a greatly reduced chance of success, as they'd be fighting each other as much as the enemy, reduced rewards on success, as they'd stop each other from doing their little reward bonus thing, and when it came to choices, you'd never know which choice they'd take - though if there was a third, bad, choice for failing to make a choice, they'd take that. They'd come back with reduced relationship modifiers as well, for you making them spend time with each other.
Conversely, if you sent two people who really liked each other on a mission together - say Anders and Justice from Dragon Age; Awakening - the opposite would occur. They'd receive a synergy bonus to success, their reward bonuses would both receive a boost for that mission, they would make a choice that largely agreed with both of them, and would come back with improved relationship modifiers.
It would encourage you to talk to and get to know your party members.
The system overall would serve as something to do to keep your party members relatively up to level, complete these quests, and be able to focus on the main story, and the stuff that is really important to save the world, but still receive the rewards for, and not ignore, the lesser problems in the world that are less urgent. It would require some good design work such that the limitations on completing missions aren't too strict and stringent that it becomes a strategy game, but that they exist enough to not let you ignore all the content, and also to make you understand and consider your party members in-role as well, such that they aren't just an off hand ignored thing. It should all make you feel like the leader of the organisation, and not unduly pull you out of the role playing experience thanks to meta reward concerns. But a deep system despite all this, would make RPGs a lot more fun to play.