Can Filemaker Do this?
The important question: Can you use filemaker to create the solution you want?
Don't know. It depends on how much time you want to invest in designing a database to meet your needs.
Filemaker is a tool for creating databases. Unless someone has already used filemaker to create the database you need, you'll have to sit down with Filemaker's "blank page" and create the database. That can involve a considerable time investment learning how to create a solution of the complexity you describe. Are you prepared to do that? Given that you have created what sounds like a spreadsheet with a moderate level of complexity, it sounds like its possible for you to create what you want if you're prepared to spend the time learning how to do it.
You might want to download Filemaker's free trial copy and try it out to get a feel for what you are getting yourself into.
I have found that if I have a working solution in Excel, I can follow the logic and calculations existing there. Using the Trial you can try it for one meal period to get an understanding. Later you will find you can have all three meal periods in the same table. Good luck with it. This forum is a great resource.