Weir, who will embark on his first season as a manager after replacing Danny Wilson at Bramall Lane, added former Walsall winger Febian Brandy and versatile Scot Stephen McGinn from Watford, plus teenagers Sean McGinty and Jasper Johns from Manchester United and Everton respectively, all on free transfers.
"We've done quite a bit of a work on these deals so at this moment there is nothing else imminent," Weir told the club's official website.
"However, if we can improve the squad within budgetary restrictions we will do. We're keeping an eye out for good players."
Weir said Brandy in particular will add a new dimension to the Blades next season.
He added: "Febian is different. He has pace to burn, he's exciting and can unlock defences. He's a contrast to what we already have in the squad.
"It's important to have a bit of unexpectedness in your team and I think that Febian offers us that. He's always thinking about going forward and that's a strength."