Hiya!
[MENTION=6786202]DaveDash[/MENTION], I just finished re-reading the magic item parts of the Hoard stuff in the DMG and couldn't find anything that gives and "X amount of magic items are assumed". Just because there are magic items in the book and just because they can be "rolled" via the tables doesn't mean they are assumed to be needed. In other words, 5e doesn't have the 3.x/4e/PF design structure of actually assuming that a "Level X character has Y number of items, giving him a CR of Z...so lets build monsters/NPCs/adventures with that in mind".
Anyway...if I was you, as I said, I'd just nix the whole attunement thing. If you just up the number, I have a feeling your players will still complain once they hit it. Upping it again...same thing. They seem to be used to just "having their cake and eating it too" without having to make any sacrifices. When the whole attunement thing was brought up in my game...maybe the second session we ever played?... one or two players balked at it at first. They figured "a magic item should be a bonus...I shouldn't be penalized for being good at adventuring or lucky...". IIRC I told them I'd revisit the whole number of attuned items if/when it comes up. It's been, what, 10 months sense we started playing (WOW! ...has it been that long?...) and we have *never* even come close to anyone hitting the 3-limit max. Yes, I am a stingy b-stered when it comes to treasure and magic, and I'm giddy with delight that the 5e designers didn't make the "magic items are assumed" mistakes that were made with 3.x/4e/PF.
Here's a neat thought: Maybe you can create "sets" of magic items that can be attuned "together"? Taking a page from the MMO side of things (I can't believe I just said that...I feel dirty now... ), maybe have the Iron Mask of Balguur, the Scale Coat of Balguur, and the Iron-Clad Boots of Balguur. If you have all three you can "group attune" them so they only count as ONE attunement slot. You could do the same with any magic item; maybe have Gloves of Missile Snaring, Ring of Jumping, and Slippers of Spiderclimb all be "group attuned" for only Rogues...everyone else has to attune them individually. Of course, giving them all names might be cooler (re: "Gloves of Nix, Jumping Ring of Nix, and the Silk Slipers of Nix the Spider").
^_^
Paul L. Ming