I have done every trip I have ever taken with just carry on. Recently, that has included a month in China and Japan and last year, a month that included Hawaii, the eastern US, Paris for a week, where I needed dressy clothes, a safari in Africa and a week in London.
So absolutely doable. The key is quick drying lingerie (Ex Officio was awesome, especially in Africa, as it dries in no time) and separates that coordinate. I used a grey Merino wool long wrap sweater (like this but in grey
http://www.backpacking-united.com/ca...p-cognac-black) that worked with any kind of outfit, dressy or casual, a super-packable shell raincoat, wore my heaviest shoes and packed the dressier ones and bought toiletries as I went.