Reinstalling my OS and getting this error “Can’t download the additional components needed to install Mac OS X.” Please help!

I'm not sure which version of macOS you attempted installing on your MacBook Pro, though you'd better install the latest macOS for your MacBook Pro with following article.

How to reinstall macOS - Apple Support

If it doesn't help, try to take your MacBook Pro to your local retail AppleStore, Genius Bar or Apple Authorized Service Provider to install macOS on your MacBook Pro there. As far as I know, it's free.

Genius Bar Reservation and Apple Support Options - Apple

Find Locations

Siggytee Said:

"Erased my disc. Reinstalling my OS and getting this error 'Can’t download the additional components needed to install Mac OS X.' Please help!"

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Troubleshooting Reinstalling the macOS:

A. Use Ethernet:

I assume you are using WiFi. So, try Ethernet, inserted to get a more reliable connection (being a directly connection to the router).

B. Having Any Backups Of your Mac?:

Important: Be certain to create a backup of your Mac prior to all of this. That way, you can have something to restore from the Mac from, should anything go wrong with the reinstall. If not, then take this as a learning experience, knowing to always do so, prior to performing any major change, scubas an update or erasing the disk.

what model-year MacBook Pro, and if 2020, what processor?

what version of macOS were you running last.

EXACTLY where are you running from now? { recovery? Internet recovery? Bootable USB-stick installer? }

what version are you trying to download and install, how did you decide what version to download?