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Short answer: Yes, you can do that.
Long answer: You’re a bit off with your lingo. First off, DigitalOcean is not a web service, it’s a hosting provider, sometimes called a VPS provider (Virtual Private Server). So you would setup whatever operating system [OS] (Ubuntu, CentOS, FreeBSD, …) and then you could install Apache. You then setup multiple user accounts on the OS, where you allow SSH/SFTP access for each user to their own directory. If you’re already doing this on a server locally, then there’s no difference, since would do exactly the same on your DigitalOcean server.
There are many great articles here on DigitalOcean on how to setup multiple user accounts and connecting them to Apache. Did that answer your question somewhat? It’s a bit broad, but hope you get it.