To upgrade your version of TurboTax, please see the TurboTax FAQ below for instructions:

How do I upgrade or switch to a higher version of TurboTax Online?

If you need further assistance upgrading, please contact TurboTax Customer Care. 

The best and most efficient way for you to connect with the right person to get the help you need is to select the version you are using in the TurboTax FAQ below:

What is the TurboTax phone number?

I don't think you can upgrade the Mac Desktop program.  You can in Windows.  You might have to call in.  But why do you want to?  All the Desktop programs have the same forms. You just get more help and guidance in the higher versions. 

Contact Customer Service

 (You need to pick the CD/Download program in the product drop down box.) 
5am-5pm Pacific Time Monday -Friday
https://support.turbotax.intuit.com/contact/

What is the Turbo Tax phone number
https://ttlc.intuit.com/community/using-turbotax/help/what-is-the-turbotax-phone-number/00/25632

I purchased Deluxe for Mac as a download from Amazon.  Deluxe worked fine as I did my wife's taxes, (married filing separately).  I needed to update to Premier for my taxes.  I upgraded by purchasing through TT Deluxe program.  I paid the $30 using a credit card, downloaded and installed.  Now the program is broken and doesn't load.  I click the icon, it bounces and shuts down.  If I click multiple times it will open the TT program.  It shows premier momentarily, but shut down.  I've tired to uninstall and reinstall my original download to no success.  I called customer service and spoke to a rep, (who was chatting online with I.T. I believe).  That was a horrible game of telephone.  The rep mentioned I.T. saying something about the upgrade for Mac was not working properly.  I had to end the conversation after two hours as I was late for work.

I'm running a 2017 MacBook Air, OS. 11.2.1 which is well within the program specifications.

If Deluxe worked on your Mac then all the versions should.  But as I said above you really don't need to upgrade.  Deluxe can do everything the Premier and Home&Business has.  And you didn't need to buy another version for your return.  The Desktop program can do unlimited returns and efile 5.  

But now since it doesn't work you are stuck with talking to support.  Or maybe a Mac user can chime in.  @macuser_22 

Thank you for the reply.

😕, I'll try contacting customer service next week as I'll most likely have to set aside a few hours or more.  The only fix I can think of would be to uninstall the corrupt upgraded program from the Mac, and reinstall a fresh downloaded copy, (deluxe or premier).

You cannot install 2 versions of 2020 TurboTax on the same computer - it is not permitted since many support files are the same.

The first version must be TOTALLY uninstalled along with ALL support files.

Here is a FAQ for how to uninstall Mac
https://ttlc.intuit.com/questions/1901210-remove-uninstall-turbotax-for-mac
Also if present remove: ~Library/Caches/KSCrash/TurboTax

Thank you @macuser_22 

I installed all of the files per the post.  The icon was still in my dock so I clicked by mistake before uninstalled the program from the applications folder.  TT opened, installed updates and Premier opened.

An error code window opened as well.  I clicked send to Turbotax and the program crashed.  It will not open again.  I'll try uninstalled the program after I delete the files.