You don't even need a powerhouse of a single computer to do that.
Windows XP running on an older Core 2 Duo system will reliably serve 3 streams if you're going from dongle-to-stream on low overhead software and not running some disgusting bloated pig of a software suite like SDR# or GQRX...
I currently run 2 feeds from one computer , 2 files of proscan , 2 external sound cards , and a 10 outlet USB hub , I also monitor 3 other scanners thru the multi port UBS hub all on 1 computer running windows 10 w/proscan
I run three feeds from two different P25 Ph2 systems using one instance of op25 on a NUC7i5. In my case I am now doing it with a single Airspy Mini @ 6Mhz, but in the past it worked equally well with three RTL dongles.
Oh and the nuc also hosts my Ubiquity Unifi server, a weather station and some other stuff....
Also running a nuc in rack - testing 6 x RTL's ( 3 x 2 RTL pairs in DSD+) on a P25 P2 system (3 x different TG lists) with 3 x Proscan stream (each pair on a separate VB cable. Also running 3 x powershell scripts that I made to allow Proscan to send DSD+ metadata as it streams.
The above is all working, next part is getting 2 x AS and 2 x AS HF shared out on same Nuc - running 3 x USB 3 active hubs.
Not sure if all the AS's will stay on same Nuc, to be fair 3 x DSD+ and powershell scripts running does make the Nuc work pretty hard.