If you have Office 2016 and try to install a newer Office product including Microsoft Project you will receive an error that they can't be installed at the same time like below.
You will need to remove the older Office before you can install the newer one.

For alternative guide see Microsofts guide at https://support.office.com/en-us/article/uninstall-office-from-a-pc-9dd49b83-264a-477a-8fcc-2fdf5dbf61d8

Removing Office

  1. Make sure you have a copy of your old Office product key that you are uninstalling if you wish to install it back later.
  2. Save all your work, this will require restarting your PC
    You will temporarily have no Word, Excel, Powerpoint, etc installed on your PC until you install the new version of office.
  3. In the bottom left search for Uninstall
    Click on "Add Remove Programs"
  4. Search for Office, then click Uninstall
  5. Click the second Uninstall
  6. Click "Yes" we want to uninstall
  7. Wait while it uninstalls
  8. Click Close
  9. Reboot and try to install the Office product again

If you arn't able to get Office to uninstall with the above steps, try Microsofts advanced tool for removing it

  1. Download the uninstall tool from Microsoft at https://aka.ms/SaRA-officeUninstallFromPC
  2. Run it when it finishes downloading, wait for it to launch
  3. Click install
    1. Wait for it to download the helper program
  4. Click Run again
  5. Read the EULA and agree if you agree
  6. Check all the Checkboxes to uninstall all the products
    Click Next
  7. Check that you've saved your work, it will reboot the pC
  8. It may need to restart the tool as administrator, click "Restart" and enter in your Administrator username and password if it asks
    1. You'll need to click install again
    2. Wait for it to download
    3. Run it again
    4. If it gets lost, click Next
      1. Agree to the EULA again
      2. Click Office, then Next
      3. Select "I have office installed but I'm having trouble Uninstalling it
      4. Yes this is the affected machine, then Next
      5. Select All products, then NExt
      6. Confirm, then Next
      7. Wait while it uninstalls Office, this will take 5-45 minutes
      8. Click Restart
  9. Once you reboot, Office will be gone from your PC and you can try installing the newer versions.