I have a 2017 Mac Pro running High Sierra 10.13.6. Is it possible for me to upgrade to mojave and possibly something that is even more updated?

Do NOT upgrade until you have made a Time Machine or other backup of your startup drive.

How to Upgrade  macOS:

The macOS version you can upgrade to depends on the year your Mac was released.

Click the  (Apple) menu at the top left of your screen and choose About This Mac.

macOS 10.14 Mojave is compatible with the Macs listed here:

https://support.apple.com/kb/SP777?locale=en_US

macOS 10.15 Catalina is compatible with the Macs listed here:

https://support.apple.com/en-us/HT210222

macOS 11 Big Sur is compatible with the Macs listed here:

https://support.apple.com/en-us/HT211238

❗️ – IMPORTANT – Backup your data, now, before you attempt an upgrade.

Learn How to Back up your Mac with Time Machine:

https://support.apple.com/en-us/HT201250

❗️ – IMPORTANT – NONE of your 32-bit apps will work in Catalina or Big Sur.

https://support.apple.com/en-us/HT208436

Before you upgrade, use this free utility to check the compatibility of your apps:

Go64: https://www.stclairsoft.com/Go64/

🖥 – Check the compatibility of your Mac with newer versions of macOS.

https://support.apple.com/en-us/HT201475

✅ - Using Safari only, download the macOS upgrade installer app:

Click > Mojave, Catalina or Big Sur.

Once downloaded, double-click the installer app in the Applications folder to begin the upgrade.

There was never a 2017 Mac Pro. Mac Pros are very different machines.

Do you mean a 2017 Mac Book Pro.

A 2017 MacBook Pro can upgrade to any of the available OS's.

For Mojave or Catalina,

Open Safari and click on this link, 

How to get old versions of macOS – Apple Support

Go to the Download OS section and click on the OS you want to install.

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS ******.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.

If you want to install Big Sur, open Safari and click on the link below.

How to upgrade to macOS Big Sur - Apple Support

If you are considering upgrading to Catalina or Big Sur be warned they do not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this free app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/ then contact the developers of the software to see

if they are offering 64bit updates.