How to prevent too many students from making appointments to meet with you when you put "Office Hours: ..., or by appointment" on the syllabus?

In the past I have included the following statement on my syllabus

Office Hours: Mon 1-2pm, Weds 3-5pm, or by appointment

However, I am beginning to get too many requests for appointments. Appointments are really inefficient. They waste both of our time trying to schedule them, and with multiple appointments per week in addition to office hours, even holding them takes a lot of time away from research. How do you accommodate students who can't make your office hours without devoting too much time to this task?

I thought about setting up a class message board where they can ask each other and answer each other's questions - anonymously if they wish - (I can also answer questions on the message board) and put on the syllabus "All content related questions should be posed in class, on the message board or in office hours. I do not reply to questions about content via email. Please schedule an appointment to meet with me if you are having difficulty getting a question answered after trying the above options"