How can I choose a specific location for Logic's 40GB of additional content?
Answer stolen borrowed here:


Download this for free: symbolic linker
Copy original 'Logic' Folder located in /Volumes/"SSDVolumeName"/Library/Application Support/ on the desired external drive and location.This is the location where all your additional content is beeing installed to.
You can delete the original folder or rename it and use it as a backup.
Use the symbolic link tool to create a symbolic link from the 'Logic' file which has been copied to your external drive.
Place the link (which looks like an alias) to its previous destination (/Volumes/"SSDVolumeName"/Library/Application Support/) and rename it to 'Logic'.
After this you will be able to download additional content.
Be aware if you want to download 30 GB of content and your SSD has just 20GB free space, it will show you the same error message because it stores the download file still on your SSD until installation is done. The solution for this is to download everything part by part."  

or: 

Using the Finders 'Go to Folder' menu option, enter:  

/private/var/folders/


A look in the various folders there will reveal a folder called "com.apple.MusicApps/audiocontentdownload.apple.com/".
Copy the folder "lp10_ms3_content_2013" to your external drive, delete the original and symlink this folder on your external drive back to /private/var/folders/../com.apple.MusicApps/audiocontentdownload.apple.com/ 
If the folder "lp10_ms3_content_2013" is missing in the original just create it on your external drive and link it back.
(not tested)