As Mike has pointed out, your biggest challenge will be screen real estate. You will be creating quite a cluttered view since the calendar web-part is not that easily customisable.
A possible solution would be to have each calendar appearing on a tab. This article will explain how to add tabs to a page
However, your challenge is maintaining each of the calendars. A better solution would be to use a single calendar and filter each view based on the Category field (which you can modify to have the groups you require).
Here is a worked example;
- Setup your page to have 2 columns
- Insert the Calendar webpart in column 1
- Insert the Calendar wbpart again in column 2
- Save the page (you need to do this to prevent the webparts being lost; an annoying problem)
- Edit page again and select Calendar in column 1; click Calendar in menu bar (i'm using SharePoint 2013); click Modify View and change the Filter to the required Category. In my example I have set the filter to Category = Meeting.
- Repeat for Calendar in column 2 and set filter to other Category; in my example filter is Category = Business.
You know have 2 views for the same calendar showing different Categories. You could combine this with HillBillyTabs2 to give flexible and expandable calendar views all driven from one Calendar list.
Hope this helps.