Setup A Computer For Multiple Remote Connections?

We have a small business that consists of 5 owners. One owner does most of the work and has a Desktop set up in a home office. They do most of the document related work. This person needs physical control of the computer for most of the day. The other four either live in different locations. They need all the information that the main computer has throughout the day. Documents that change, New documents, and the ability to change anything in the documents and save them. The way its setup now is a remote login. This is extremely inconvenient since the main computer is basically hijacked when someone remote log ins. Each computer is obviously on a different network, so local networking wont work.

Is there a way that the main computer can be on, being worked on by the main person, but still be accessed by the other people at the same, or different, times to get the updates and new documents? Can we do this with what we have, or is there another way to do it?

We have thought of various things, like severs, remote log in programs, etc. But nothing really works the way we need. The closest one we found was an auto sync program. But it requires everyone to have all the files on their computer. This is slightly inconvenient because theres thousands of documents and things that everyone would have to load when one person may need 1-200, and the other needs 200-400.