Ryan Shawcross and Robert Huth formed a successful partnership at the heart of Stoke's defence last year, but Pulis has signed one more centre-half in Woodgate and has now confirmed he wants another.
Shawcross has been named the Potters' captain for a second successive season, yet Pulis has warned the 23-year-old that will not guarantee him a place in the team.
"He won't be treated any differently to anyone else if his form dips," said Pulis in the Stoke Sentinel.
"So if we bring in another centre-half, like I still aim to do, he will have to fight like mad to keep his place."
Pulis does feel, however, that having the armband again could help Shawcross as he looks to force his way back into the England reckoning.
"I'm giving him the captaincy back and I'm hoping he picks up the baton again and continues getting better every year," added the Stoke boss.
"It's a great honour for him and one he took on board when he was made captain last year.
"He's got a long way to go still and understands that himself, but he has to come out of himself a bit more as he continues to grow as a footballer and a man.
"The big thing with Ryan is that he's got that carrot dangling in front of him in the shape of the European Championships next year.
"If he has a top, top season with us, there's no reason why he can't get into the England squad in time for that.
"Having Jonathan Woodgate around can only help him in that direction too."
Shawcross admits he does not feel "too wanted" by England at the moment but is determined to make an impact for the Three Lions, having told Wales boss Gary Speed he has no intention of switching allegiance.
"I have spoken to Gary Speed a couple of times and made my plans clear," Shawcross told Stoke's official website.
"He is a very good, young manager and I have a lot of respect for him, but I made my decision a long time ago when the current rule wasn't in place that I could play for Wales.
"Obviously he wants me to play for Wales but I made a decision and I'm going to stick with it. Hopefully I can prove I am good enough to get into the England team.
"I'm not in the England team at the moment so I don't think I'm too wanted there. It is good that Wales want me but this rule wasn't in place when I made my decision.
"My decision might have been different if the current rule was in place at the time but these things happen."
Stoke's Europa League campaign gets under way on Thursday night when they take on Croatian side Hajduk Split at the Britannia Stadium in the first leg of their third qualifying round tie.