I want to install macOS Mojave on a partition on my new macbook Pro that runs Catalina on startup HD. Why I can't download Mojave install for App Store?

Do you still have your old MacBook Pro? If so, follow these instructions to create a bootable flash drive for Mojave, then add a Mojave volume on you new HD (assuming it's formatted as APFS) and use the flash drive you created to install Mojave on your new MacBook HD Mojave volume. You can disregard the instructions for upgrading to Catalina, since you already have it on your new MacBook.

You’ll need a blank 16MB or more flash drive. If your flash drive has files on it back them up before using the drive for this purpose because the drive will be wiped during the process of making it bootable. Use your old MacBook with Mojave on it to make the bootable flash drive. Then transfer the flash drive to your new MacBook to install Mojave on the new volume that you will have created on your new MacBook.

1. Make sure you’ve updated Mojave to the latest version.
2. Back up your computer (I used a Time Machine backup to an external drive).
3. Download a copy of the Mojave installer at this link: https://itunes.apple.com/us/app/macos-mojave/id1398502828?ls=1&mt=12 This link will take you to the Apple App Store’s hidden page for downloading Mojave. Note: IT WILL ONLY WORK IF YOU HAVE NOT ALREADY UPGRADED TO CATALINA! If the installer automatically starts after downloading, quit the installer (Cmd-Q will do it). You don’t want to proceed with the installation yet.
4. Insert your flash drive into a USB slot on your computer.
5. Open Finder and navigate to Applications/Utilities/Terminal and open a Terminal window. In the Terminal window type in “sudo” followed by a space (no quotes).
6. Now open a Finder window next to the Terminal window and in Finder navigate to Applications/Install macOS Mojave (which you downloaded in step 3). Right click on Install macOS Mojave and click on Show Package Contents.
7. In the Contents window navigate to Contents/Resources. In the Resources folder find createinstallmedia and drag it into the Terminal window. The necessary command will be added automatically.
8. Next, type - -volume (dash, dash volume) followed by a space.
9. Click back to your Finder window and select Go from the menu bar. In the Go menu select Go To Folder (near the bottom). In the pop-up window type /Volumes and click Go. Then click on the name of your flash drive and drag it into the Terminal window. That completes the necessary command in Terminal, so hit Return and it will ask for your password.
10. Enter the password you use to unlock your computer and Terminal will ask if you wish to continue. Type y for yes and press Return. Terminal will now erase your flash drive and install the Mac OS Mojave installer. It may take awhile, depending on the speed of your computer, but when finished you will have a portable, bootable Mojave installer.

Now that you have your bootable copy of a Mojave installer, you can upgrade your computer to Catalina. The easiest way is to click the Apple symbol in the upper left corner of your screen and choose App Store. When the App Store window opens click on Updates and the option to install Catalina should be there. Click on it and follow the prompts to install Catalina on you system.

Once Catalina finishes installing, you can use Disk Utility in Applications/Utilities folder to add a new volume for Mojave on your hard drive. If you need instructions for adding a new volume to your hard drive, follow this Apple link:  https://support.apple.com/guide/disk-utility/add-erase-or-delete-apfs-volumes-dskua9e6a110/19.0/mac/10.15 

When you’ve added your new volume for Mojave on your hard drive, make sure your Mojave installer flash drive is still plugged in and restart your computer while holding down the Option key. When the choices appear, select Install MacOS Mojave and when asked where to install it, select your new Mojave volume on your hard drive. That’s it! (I didn’t say it was easy, I said it was the best way to have both Mojave and Catalina running on the same Mac  ;-).

Now you can run any older 32-bit apps on your Mojave volume and everything else on your Catalina volume. To change between volumes, open System Preferences, select Startup Disk, enter your password and select the volume you want to use. Then select Restart. 

FWIW, it's never been possible to run a version of macOS/OSX earlier than the version a Mac was shipped with. What you can do is install Mojave as a VM in Parallels Desktop, VMWare Fusion or VirtualBox.

In general, you cannot run an older OS than the one that shipped with the Mac.

This is because the old OS doesn't know anything about the newer hardware in the new Mac. Apple doesn't retroactively update older OSes to make them aware of the newer hardware that is in the newest shipping Macs.

So, even if you were allowed to download it and install, it wouldn't work.

https://discussions.apple.com/thread/251545730