First- and second-round leader Storm shot a 69 to stand on 12-under alongside Scotland's Scott Jamieson (66) and Spaniards Gonzalo Fernandez-Castano (66) and Pablo Larrazabal (64).
Jamieson and Larrazabal will be in the tournament's final grouping on Sunday.
Fernandez-Castano - who hit four birdies and five pars on the back nine - Jamieson and European Ryder Cup team member Peter Hanson had been three strokes off the leader after round two. The Swede now stands alone in fifth, a shot off the leaders, after shooting a 67.
Richie Ramsay and Danny Willett are tied for sixth while Henrik Stenson and Nicolas Colsaerts, who will make his Ryder Cup debut for Europe at Medinah in Illinois in late September, were tied for eighth.
The other Ryder Cup team member Martin Kaymer stands six shots adrift of the leaders after shooting a 68.