The Baggies have done well in the market this summer with John Swift, Jed Wallace and Okay Yokuslu all arriving as free agents.
Bruce, though, wants a couple more with his squad looking light up front and at centre-back.
Any arrival, though, is likely to arrive on loan with Bruce admitting the club hasn’t got millions to spend on new recruits.
“My job never finishes with that – we are greedy,” the boss said when asked if he wants more signings.
“We should never be happy with what we have got. I would like to bring in a couple more if we can.
“There is still a long way to go in the window.
“And the big clubs are now coming back from tour and the young lads who they will be letting out on loan – they will have been assessed.
“We’d like to do a couple more, we’ll see what happens.”
Asked if he is limited to the loan market, Bruce said: “We knew the market and I knew the market.
“I think I was honest with the supporters – loans and frees are where we are at.
“I never expected us to be signing players for millions but I think that’s up and down the championship. Not a lot has been done really. I think clubs are still feeling the effect of Covid. That is still biting away.
“We have to be in that market, we have to be a bit clever.
“But the big clubs now are just starting to look at their young players. We have scoured that market and we have got one or two bits going on.
“We’ll see what happens over the next week or so.”
Bruce reiterated some players may have to leave to help fund additions.
But he said getting players in is his biggest priority.
“That might be inevitable too,” the boss said on departures.
“One or two have left. That’s normal.
“We want to add to the squad really but if one or two have to make way that’s got to be it.”