Goku uses this technique when confronting Frieza, Cell, King Cold, and the Ginyu Force in Hell. He uses the power to defeat the Ginyu Force and prepares to fight Cell until Pikkon attacks and defeats Cell in a few hits.
Later, in Dragon Ball GT, Goku appears to use the power up when starting his fight against Frieza and Cell in Hell, as his aura is yellow. During the battle with Naturon Shenron, Goku briefly uses Super Saiyan power while talking to Naturon before transforming to Super Saiyan 4.
Video game appearances
"Super Saiyan power" was named for this kind of ability to transform to two different forms in Dragon Ball Heroes. The ability makes it that, if Goku transforms into Super Saiyan on the second turn after a Kamehameha, power is +2000, or +5000 if it is greatly successful, transforming him into Super Saiyan 2.