If you have 1 and only 1 SP* then yes, you can have that 1 guy pitch every 4th day and the rest will alternate over a 5 day period.
Game 1 LH*
Game 2 RH 1
Game 3 RH 2
Game 4 RH 3
Game 5 LH*
Game 6 RH 4
Game 7 RH 1 (5th day)
...but if you have 2 SP* it will not work
Game 1 LH*
Game 2 RH 1*
Game 3 RH 2
Game 4 RH 3
Game 5 LH*
Game 6 RH 1*
Game 7 RH 4
Game 8 RH 2
Game 9 LH*
Game10 RH1*
Game11 RH3 (7th day) - no good