If you have started a message exchange with an office, you can click on the “> Propose a Booking” link which appears at the end of their last message to you. This will allow you to choose any date and start/end time that you want, even on days that are shown as unavailable to other offices, except those dates where you already have a confirmed booking. You can also propose whatever hourly rate you want.

If the office accepts, then you have a confirmed booking and all of your other applications and proposals will be canceled for that date.