I’ve always hated “rod of seven parts” type missions. Go out and find many pieces of this one thing and then put them all together at the end. It always seemed wrong to me that so many items of power were split into multiple pieces that would all still function if jammed back together. I dislike them because I think it shows a lack of GM (or author) imagination, and by the time you hit piece five or six, the players are bored and just want it to be over. I think any time you make the party do the same thing more than three times, you’ve lost them.
So do I not believe in campaign continuity? Absolutely not. I believe that campaigns really need a form of continuity or they become a chaotic mishmash and prevent character growth. By growth I am talking about role-playing ideals, and not experience and gold farming. If nothing other than building your list of contacts, then at least you’re showing some history building.
So how would I do an item of many parts mission, assuming I thought that was something necessary? I think first they need to learn that it exists. If some wise scholar comes up to them and tells them about it, then are they just getting the stuff so he can have the item? If not, why would he tell them about it? If you’re going to spend that much time working on something then it should be pretty important - like save the city important. So let’s assume that an ancient enemy of the player’s hometown is marshalling their forces and getting ready to move invade. But someone (hopefully a player character while on a different mission) stumbles onto a find of some historic device, maybe either an artillery weapon of some kind, but in order to build it, they need all sorts of really strange parts, and they need them yesterday.
Now the players can go out on different sorts of missions to acquire the parts, but there should be other teams out doing the same. Maybe the “bowstring” on this thing needs to be dragon tendons because nothing else is strong enough, so they go out and kill some dragons. Meanwhile, another team goes out to get the granite needed to form the thing’s base and another team goes out to buy raw industrial diamonds for the ammo. So upon returning, they find out that steel isn’t strong enough so they need to go and purchase some magical metal from the dwarves, but they expect the dwarves to be jerks and maybe not let them buy what they need. Turns out the dwarves are cool about it, but at some point on that journey, the enemy has sent a hit squad to stop the party from succeeding, so they get their fighting, just not how they expected. But they return to find out that the diamonds were stolen by a bandit group before the other team got there and that team is now tracking the bandits through some major forest. So they have to go and basically bail out that group because they are really all captured by the bandits by now.
Meanwhile, back at home, the city has been besieged. They are all working feverishly on building this thing(s), but without the diamonds for ammo, it won’t work. So after the party kills the bandits, recovers the diamonds, frees the other team, now they need to break into their own city through the siege. They also probably have to fight through some scouting parties sent out by the attackers as well. And don’t forget that one of the hit squad got away and is now following them and basically calling in all sorts of trouble against them whenever they can, so they might want to take care of them as well.
What did I change? Well, first of all, I think it makes more sense that if it were really important you would send multiple teams. It makes it more fun to find that one of them needs to be bailed out. The time pressure typically adds to the excitement, especially when they effectively fail at meeting the deadline. These are not all - kill dragon-like thing - take body part missions. (It’s not an MMO for crying out loud.) There was one of those, then a trade mission (with spies), then a rescue/recovery mission, then a war game mission. Then once the thing is built, it may help turn the tide of the battle, but it isn’t going to do it all by itself. The party will still need to fight in the final decisive battle, and the artillery weapon may be helping, but will not directly aid them. It’s not like each of them just picked up a super duper magic sword.
As always, these are just thoughts intended to give you ideas and make you think. Take a strand of what I laid out here, make it your own, and run with it!