Same day stand-by (earlier or later flights) is allowed, unless prohibited by the fare rules.
But, I have had mixed results/responses. Back in June 2001, when I tried this at Green Bay, WI, they said NO, outbound cannot be changed, only the return. Never a problem at hubs MSP/DTW/IAH etc. One time in IAH, an NW agent (presumably new) said a $100 change fee is involved for the outbound! But a polite request to check with her supervisor or an experienced agent got the stand-by for me free! So, keep asking till you get what you want.