Does Big Sur work with the 15 inch mid 2014 MacBook Pro?

Yes—Big Sur states that you will need 35.5 GB of free storage when upgrading from High Sierra or newer, and 44.5 GB when upgrading from an older versions.

Big Sur macOS 11.0.1

https://support.apple.com/macos

App Store:

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

How to upgrade to macOS Big Sur w/tech specs

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

Tech specs:

• 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)

https://support.apple.com/kb/sp833?locale=en_US&viewlocale=en_US