This is what is so great about my Suzuki Burgman 650. It has HUGE storage under the seat. I commute to work in my normal work clothes (casual to business casual) with a leather jacket and textile overpants on, boots, etc. I keep my day shoes in my gym bag, which when full of my gym shoes and usual work out gear and day shoes, fits in the trunk of the Burgman. Get to work, stuff the helmet and gloves under the seat, carry in the gym bag, strip off the over pants and jacket and put on my day shoes.
I haven't quite got it down on the GSA yet, but that stuff will fit in the side boxes. I might get a large tail bag. It is kind of a bummer that there is no built in storage on the GSA.