The idea from scribblecrumbs on tumblr was:
yeah but imagine Pietro falling asleep in the weirdest places because he gets so exhausted after running for a long time
and imagine him doing it in the Avenger's Tower
now imagine the Avengers finding him in the most random of places
So here's my take on it!
Tony likes to work on the floor when he's doing a big project so he can spread out his blueprints and his notes everywhere. It's easier than finding a big enough table, and this way he can crawl around to grab things rather than moving around in a chair. Bruce knows to walk around them, and everyone else just stays out of Tony's space in general.
Apparently Pietro didn't get that memo.
Tony's staring at the floor with his mouth open, shocked into a rare silence at the sight of the older Maximoff twin sleeping on his papers like a cat. The kid is under the table at least, but Tony had papers everywhere and now the ones he wants are lodged somewhere under Pietro's unruly brown and blond mop of hair. Tony puts his morning smoothie down on the table and is looking around for a stick he can prod the kid with when he sees the telltale sign of drool. On his blueprints.
So unfortunately, the entire tower hears Tony holler for Wanda.
Steve and Sam:
"So what do we do?"
"I guess we leave him."
Sam and Steve were going to play a round of pool on a Saturday off, something they did often once Sam realized that Steve liked the quiet companionship. Sam had shown up bright and early and brought his cue and a case of beer for the both of them, only to find Steve sitting on a stool with a bemused smile as he looks at Pietro sleeping under the pool table. Pietro's arms and legs are tangled with the other stools, his shoes half off. Sam winces in sympathy when he sees the way the kid's shoulders are twisted up, and he looks around until he spots one of the smaller throw pillows on the couch.
"Here, can you give me a hand?"
There's not enough room for Steve's broad shoulders in the limited space under the table, so he ends up with the pillow while Sam manoeuvres himself in a way where he can lift Pietro's upper body just enough to adjust him into a more comfortable position while Steve slides the pillow under the kid's head.
It's a more delicate operation either man has done recently, and afterward they sit out on the landing pad with their beers, pleased with themselves. Pietro wakes up later with a pillow, Steve's jacket, and only a minor crick in his neck.
Clint habitually spends a lot of time in the upper floors of the Avenger's Tower, keeping watch and practicing his aim. He keeps odd hours too, so he often sneaks around in the dark on his way to the roof. He says it helps keep him in practice from when he was a spy, but even so he no longer takes a route near Natasha's bedroom after he startled her the one day. He still has the bruises to show for that.
It's ten to four in the morning, and he's on the way to the roof when he sees something dark and lumpy lying in front of the door. He drops back immediately, and is about to notch an arrow to his bow when the shape snores.
Clint groans, and turns on the light that illuminates the door. Pietro comes awake with a babble of sleepy Sokovian and Clint claps a hand over the kid's mouth so he doesn't wake the whole tower, and hauls him off to his room and dumps him into bed. Pietro doesn't even notice that he's not in his own room, and goes back to sleep muttering what Clint is sure is an insult. The sharpshooter almost wants to flip the kid out onto the floor and make Wanda come get him, but it's too early for that shit.
He can't even be bothered to go back out for target practice at this point, and he ends up commandeering the couch on the main floor instead.
Bruce is still a little leery of either twin, and he usually tells Steve if he finds Pietro camped out in his lab, on the stairs, or face first on the kitchen counter. Eventually he starts feeling exasperated rather than apprehensive, and he buys a stack of light fleece blankets the next time he's out getting supplies. Bruce tapes reflective strips on them so they're easily seen even in the dark and rather than calling Steve, he tucks them around Pietro whenever he finds him.
Thor finds Pietro sleeping behind the couch one day, after he trips over the boy's protruding feet.
"That is no place to sleep!" Thor says in his cheerfully loud and frank way, and he picks up Pietro as if he weighs nothing.
Tony, Clint, and Natasha maybe find it a little too funny the way Pietro tries to squirm out of Thor's arms, squawking about how he is too old to be carried like a little child. Thor just laughs and carries Pietro to the twin's room, regaling him with tales of when he and his companions in Asgard once encountered a sleeping spell. No one finds Pietro sleeping on odd places for a whole week afterwards.
Natasha is in the same room one day when Tony trips over a sleeping Pietro, and she's so fed up by the tantrum that Tony pitches that she starts making designated sleeping areas for the Maximoff boy.
She does it without telling anyone though, and in truly understated style. Soon Pietro has no less than fifteen different hidden places he can crash in, and the rest of the Avengers only figure out where about six of them are by following Pietro's snores. Clint manages to find two on his own, but the team never knows just how many Natasha made around the Tower.