It's possible, but it you want to integrate starter solutions, it's not a simple process.
There are two basic approaches:
a) keep your separate files as the location where the data is stored, but select one file (or create a new one) where you set up table occurrences that use external data source references to refer to the tables in the other files. This enables you to use a table of contacts from the contacts management file as your table of contacts in your event management file, for example. The trick here is that if you already have a contacts table in your Event Management table, once you've added the new contacts table occurrence, you'll need to modify relationships, scripts, layouts, calculations, value lists, etc to refer to the new table occurrence in place of the old.
b) move all the tables, layouts, etc into a single file. This can be done but it's a lot more work than a) and requires a thorough understanding of FileMaker and of the design of your current files (which is where this becomes a challenge when using starter solutions as they aren't files you or I designed.) FileMaker Advanced becomes pretty much a necessity as well as the Database Design Report becomes a very useful tool for checking your work for broken and missing links between buttons and scripts and other design issues. While you can copy and paste groups of layout objects (including all objects on a layout), can import scripts and individual tables. Much of the original designs have to be recreated manually such as relationships, Layout part dimensions etc. And the process of recreating a complex layout from the original file in your new file is a process that requires careful attention to detail and to the sequence in which you bring over not only the layout objects, but the scripts any buttons or script triggers perform or you end up with a layout where a lot of buttons and triggers are disconnected from the scripts they perform.
Here's a thread that outlines moving a layout from one file to another just to give you an idea of how you might do this: Importing Layouts
I've also heard of a tool called FMMigrator. Haven't used it. Don't know what it costs, but it is supposed to make this process simpler so you might research it.