How to update macOS HighSierra 2016 MacBook Pro from version 10.13.6 to version 10.15 or later?

First make a recent backup.

Start up from macOS Recovery

Command-R 

In Disk Utility>View, select Show all Devices, highlight the top left entry.

Run Disk First Aid on all items in the left panel, from top down.

Then restart & go for whichever OS you want.

MacOS Catalina 10.15.7 - Technical Specifications

General Requirements

OS X 10.9 or later

4GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013 or newer)

How to download and install macOS - Apple Support

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

macappstores://apps.apple.com/app/macos-catalina/id1466841314?ls=1&mt=12

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

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

macOS Big Sur - Technical Specifications

General Requirements

OS X 10.9 or later

4GB of memory

35.5GB available storage on macOS Sierra or later*

Some features require an Apple ID; terms apply.

Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Big Sur:

MacBook (2015 or later)

MacBook Air (2013 or later)

MacBook Pro (Late 2013 or later)

Mac mini (2014 or later)

iMac (2014 or later)

iMac Pro (2017 or later)

Mac Pro (2013 or later)

Learn about compatibility and how to identify your specific Mac model

https://apps.apple.com/us/app/macos-big-sur/id1526878132?ls=1&mt=12

And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...

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

Monterey…

macOS Monterey is compatible with these computers - Apple Support

• iMac – all models from late 2015, iMac 16,1 – 20,2
• iMac Pro – all models, iMac Pro 1,1
• MacBook & MacBook Retina – all models from early 2016, MacBook 9,1 – 10,1
• MacBook Pro – all models from early 2015, MacBook Pro 12,1 – 17,1
• MacBookAir – all models from early 2015, MacBook Air 7,1 – 10,1
• Mac Mini – all models from 2014, Mac Mini 7,1 – 9,1
• Mac Pro – all models from 2013, Mac Pro 6,1 – 7,1

https://wpbeaches.com/apple-minimum-system-requirements-for-macos-monterey-12/

https://apps.apple.com/us/app/macos-monterey/id1576738294

macOS Monterey on the App Store (apple.com)

https://apps.apple.com/us/app/macos-monterey/id1576738294?mt=12

Monterey full installer.app

Why does OSX Monterey 12gb download turn … - Apple Community