I don't commute to a dressy office, but I do commute in cycling clothes and carry my work clothes in a pack. To reduce the amount of stuff that I carry while riding, I leave my work shoes at the office (I ride with my cycling shoes) and change when I get to work. I also leave a small blowdryer at the office so I can dry my hair after showering. I leave a couple of nice sweaters/blazers at my office for use if needed and occasionally I stash some additional clothing at the office over the weekend for use during the rest of the week. Also, I keep spare undies and socks at the office in case I forget to bring these.
When I lived in Washington Dc and had a suit-only job, I had use of a closet at work and I kept most of my suits at work. I'd commute in part of my outfit for the day (blouse, sometimes my suit skirt/pants), then change into the rest of my suit when I got into work.