Is is possible to use iCloud as a virtual server?

We are a three-person design agency and currently use a server that we store, work on and save our files to in real time. If we want to work remotely, we have to log in. This is very stable and files often get lost ⚠.

We are trying to find a cloud-based service that we can use for this same function so that we can begin to work remotely from home, while on vacation, etc. Ideally, we want a solution that allows us to store, work on and save files in real time. We don't want a solution where we have to keep downloading, working on and then uploading files. Does that make sense?

I'm not sure where to start. Any help would be awesome! We use the typical Adobe Creative Suite software. We are not looking for solutions that allow us to work on phones or iPads. We would be working on desktops or laptops.