The answer to a CPU supported by your system and Windows 11 is no -- and the chances of finding a drop-in replacement board (which would have to come from a successor Precision model) are very low.

You can find complete, used 3630 model (and up) starting at about $150, making any upgrade effort economically questionable and a board-only replacement effort quesionable.

Although the Precision 3620 is not officially support, you still can install Windows 11 to extend the life of the system usage.

For hardware settings, set boot mode to UEFI, enable Secure Boot, enable TPM.

For software preparation, download latest Windows 11 ISO, download latest Rufus.  Run Rufus to create Windows installation media.  Select Rufus option to allow local account setup and option to disable Bit Locker.  User account and Bit Locker can be setup later.  When complete, the installation media should allow you to perform a clean install of Windows 11 without any bypass.

@Chino de Oro​ As with most upgrades, I assume it is prudent to do a complete system backup before this upgrade. The Skylake processor does not have the required security features. Will this cause any problems with Win11?

Yes.  You would need to bypass the TPM and CPU checks to install Windows 11 in unsupported mode.

@Hank4​  You'll only receive a few updates and that's it.  When new Win11 builds come along, it won't update.  This is my experience having Win11 on unsupported hardware.

Luckily, the Microsoft site always has the latest build for download.  Be sure to do it as Chino said.

Sigh!!! ... If I were the only one who used this computer, I would probably proceed. However, the fact that there will be at least one other user that depends upon this machine dictates that it must run as dependably as possible. That being the case, it seems that I must go ahead and build or purchase a Win11 machine. Thanks to all who replied to information request!

If you do purchase a Win11 PC, make sure it has 8th Gen or newer CPU.  There's sellers that have Win11 on unsupported hardware.

In my case, I bought a Precision 3420 with Win11.  I thought it would still have all the updates - nope.  So I put McAfee security on it to keep it secure.

I also own a 3620 and just left Win10 on it.  There's 2 options.  Microsoft has an extended updates for a year option.  2nd option being one can run their own security like McAfee or Norton just to name 2.

@Hank4 , sorry for late reply.

As with most upgrades, I assume it is prudent to do a complete system backup before this upgrade

The easiest complete system backup is to remove your current boot drive.  Then installing a small SSD (prefer NVMe for its fast performance) and install Windows 11 on it.  Test use it for a few days and if you don't like it, just swap back the old boot drive and your system will be just like today.

The Skylake processor does not have the required security features. Will this cause any problems with Win11?

Windows 10 or Windows 11, it's just operating system.  Windows 11 will install all drivers and function that available from your system hardware.  Your 3620 has UEFI boot mode, Secure Boot, and TPM.  They are fully compatible to install Windows 11 (if you follow my instructions from previous post).

As for your latest post, am not sure if you read and understood my earlier post but I did mentioned that you can add multi users accounts as you want.  

The 3620 I worked on is still performing excellently with the latest Win 11 Pro for Workstation and it has been receiving all monthly security update from Microsoft.  

Since the 3620 system is not officially support by Microsoft, I don't want to persuade any users to upgrade to Windows 11 not knowing when MS will cut off the support.  I only suggest it as a low cost option to extend the useful life of your system.

System hardware at a glance

Windows version

Monthly security update from Microsoft

System security at a glance

@Chino de Oro​  You're lucky to be getting security and build updates on your 3620.  Makes me wonder how Blind Center of Nevada installed Win11 on my 3420.