It's only 20 people. The company culture is such that sabbaticals are available. Ten simultaneous sabbaticals is everyone's problem because: those that aren't taking a sabbatical will get short changed in terms of time away and more work. Those that take a sabbatical may not have a company to come back to a year later.
My first thought is to get everyone together and describe the situation: ten people want sabbaticals next year; it is a potential problem for the company; and everyone together can seek something equitable and acceptable and reasonable that will work over the short and medium terms.
My gut is that among the ten people seeking sabbatical, some are not certain they will return. That is the second part...meeting with each person individually to discuss the reasons they are asking for a sabbatical now. Was there a deathmarch to release? Are they unfulfilled? Is it something that can wait a year? Are just toying with the idea of a sabbatical?
Good luck
If they want to travel, they need to be completely off and you can grant it to some people.
If they want to work on some side project, then say no to some of them but propose a part-time job (work 2 or 3 days a week). Make sure to explain why you are saying no (can not afford to give half the staff a year off).