That depends on the design of your databases and how you intend to use them. What is the reason for having 3 separate databases that merge into one master database? If you can host a single database that all users can connect to and use as clients of that one database, the process will be much, much simpler. And FileMaker Databases can be accessed over the internet so this is possible even for iOS clients "out in the field" if they have decent cell phone coverage where they are using the system.
Merging your data can be done with data imports--provided you set up primary keys with Get ( UUID ) instead of an auto-entered serial number to ensure that they are unique in each copy of your database, but problems arise that are not easily handled if user 1 modifies a record for John Smith in one fashion, user 2 modifies the same records for John Smith in a different way and then the data is then imported back into the master copy.
You may want to evaluate 3rd party products (both 360Works and SeedCode offer them) designed to automate such a synch process.