The games will be the first chance Iron fans will have to see the three summer signings Joe Murphy, Dave Mulligan and Ramon Calliste.
As well as Stockport, UE San Antonio and Carlisle United are also taking part.
Carlisle opened the tournament with an 11-0 win over the Spanish side on Monday night
United will play again on Wednesday in the 3rd/4th place play-off with the local side if they lose to the Hatters, or in the final against the Cumbrians on Thursday if they win.
Iron boss Brian Laws will not play his strongest team, and will rotate his players during the matches - regardless of the score on the pitch.
"The games we will play are against teams who are good opposition for us at this stage of pre-season," he told the Scunthorpe Telegraph.
"They're not going to be physical games, no-one wants that. The important thing for all the teams here is not to get injuries, so no-one will be going in stupidly.
"We'll give everyone a run out. I don't want the players, if possible, playing the full 90 minutes just yet."
One familiar face in the Stockport line-up will be left-back Michael Rose, who spent the second half of last season on-loan at Glanford Park.
He joined Jim Gannon's side this summer after being released by Yeovil Town.
The Hatters include two trialists in their side - 17-year-old Irish goalkeeper Carl Coleman and left-winger Martyn Woolford.
