Having grown up on earlier editions it's taken me awhile to adjust to 5E's magic item philosophy. I've been leaning towards items that scale with the players, unlocking new powers as they level up and deepen their attunement with them. Especially weapons, which I've also taken to naming. It feels like my players form much deeper attachments to them.
My roommate (who is also one of my players) thinks it would be cool if I threw in 5 rings into the game: Earth, Wind, Water, Fire and Heart. He wants them, when collected, to be able to summon whatever the DnD version of Captian Planet is (a Solar?) lol. I thought the Captian Planet idea was stupid (albeit hilarious) but I did consider giving them the different rings that would scale with level. At level 1-4 they add a minor ability (e.g. heart gives +2 to all healing spells cast) 5-9 more powerful (lvl 5 fireball for the fire ring), 10-14 still more power etc etc. Something like that might be interesting to throw in.
I haven't considered what the trade-off for the Staff of Focusing is yet (I'm actually considering deleting it altogther given some of the other loot they're going to find) but good ones that allow you to scale power might be spell slots (e.g. permanently sacrificing a 2nd lvl slot unlocks power X and a 5th lvl slot unlocks Y). This is also nice because 5e has spells more centric to classes than 3.5 for example, so more classes would be able to use it effectively.
Alternatively you could use something like Ioun stones to power higher level abilities. The PCs have to find the stones (side quest) and then have to choose between using the stone as it is or using it to power the bigger item.
If the item is intelligent you might have to teach it something that has to do with its powers or purpose. For example the Staff of Focusing was made by an alchemist, if it was intelligent and they wanted to use its powers they might have to teach it a new recipe. Something like that.
And finally, theres always the classic "bathe it in the blood of X" to unlock powers. Good items might need to slay fiends, Evil items might be a helpless person. It depends on the item and the setting and the story.
