...there is a Microsoft Online and Office Online Server (OOS) available for organizations, but it's not cheap. Basically, the standard version of Office wasn't designed to be used from a server but was instead set up as an "end-user" program. I've worked with some large government entities and they all used versions of Office which were installed on individual machines, mainly because the server/online versions were problematic and expensive to maintain. Read about it in the links below:
https://blogs.office.com/2016/05/04/office-online-server-now-available/
https://support.microsoft.com/en-us/help/257757/considerations-for-server-side-automation-of-office
In regards to Adobe, I believe there is an Adobe Acrobat Elements server edition for PDF file creation, etc.. Or at least, they used to. Once again, utilizing this requires a special edition of Adobe, not the individual user-end installers. And although I don't use it, they now have a "Creative Cloud" offering which offers Photoshop usage, etc. Check with the Adobe's site for their offerings.
https://creative.adobe.com/plans?promoid=49F59RVM&mv=other
Hope this helps.
Grif
How can I setup a computer so that different people on my home network can access the programs on it at the same time?
Let's say it's a software server so I install the Adobe suite and Microsoft office oh a single machine so that I don't have to install it on the individual machines of my family members and they would just be able to log into this virtual server from their personal machines and use the programs whenever they need them as individual users on that one computer remotely from their own computers.
So multiple people can access the programs on this main server from their personal computers and save whatever they need back onto their personal machines...

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic