Q:

How can I have 2 versions of the same .wsp activated on SharePoint 2016

Scenario: SharePoint 2016 MinRole Farm with 1 FE with Distributed Cache and 1 App with Search. Dev and Prod farms with the same specs.
Steps in Test Farm: 

Create a site using activated custom template Original.wsp and modify it.
Save site as template and generate OriginalNew.wsp that gets activated in solution Gallery as part of the save process. 
Download OriginalNew.wsp to my local PC

Steps in Prod:

Upload OriginalNew.wsp to Solutions Gallery
Issue found: OriginalNew.wsp has same solution id than Original.wsp and the Activate btn is not enabled for it.  

Question: How can I have both versions activated if they both are having the same ID? Or should I use another procedure than the one described to obtain the same results?

A:

First, It's not possible to have 2 solutions with the same solution ID on the same farm.

In your scenario, 

Unfortunately, you don't have SharePoint solution to open it with Visual Studio and change the Solution ID easily!

Check also Difference between Feature ID and Solution ID

So the available workaround is changing the Solution ID and rebuild the WSP fil again as the following:

Rename WSP file to CAB and extract all the files
Using  7 ZIP tool to open the cab file.
Modify the manifeast.xml and change the Solution ID.

Rebuild the correct directory structure for the solution as mentioned at Rebuilding a .WSP File in 4 Easy Steps

