Out of curious, using a 32GB USB for only one OS installer is really wasteful, so here's a guide for you guys to make full use of it :)

Example in this guide:

• A 32GB USB
• 4 OS X/macOS installers (Mountain Lion, Yosemite, El Capitan and Mojave)
• Host machine is Mojave (Laptop Haswell i3 U chip)

How to get those installer?

• For ML, Yosemite, El Capitan you download them from this link with Safari
• For Mojave (and Catalina), use dosdude1 patcher to download the full .app file. The installer from App Store in my case only download a 14MB file.

Preparation

• Check your SMBIOS FIRST!!! For compatibility, or your machine will get error with the installer. In my case is an i3 4005U Haswell, there are 3 models: MacBookPro11,1 MacBookAir6,2 and MacBookAir6,1 If I choose MacBookPro11,1 I cannot extract Mountain Lion because it is not supported for that model (only Mavericks and above). So I have to change to either MacBookAir6,2 or 6,1
• Open Disk Utility -> Erase your USB in Mac OS Extended (Journaled) -> Create partitions with same size that is 8GB, so with a 32GB you'll have 4 partitions (Untitled 1, 2, 3 and 4)
• Extract the .dmg downloaded to get the installer .app file, place them in Desktop
• Rename the installer .app file based on their version. I rename them ML.app Yosemite.app ElCapitan.app and Mojave.app

Here's where I will install them OS X:

• Mountain Lion -> Untitled 1
• Yosemite -> Untitled 2
• El Capitan -> Untitled 3
• Mojave -> Untitled 4

Mountain Lion (Mavericks and below)

Right click on ML.app -> Show Package Contents -> Contents -> SharedSupport and you should see InstallESD.dmg copy and paste it to Desktop

Open Disk Utility -> Right click on Untitled 1 volume on the left -> Another panel appears saying Would you like to restore to “Untitled 1”? now click Image... and choose InstallESD.dmg from Desktop -> Restore. After that you have one

Yosemite, El Capitan and Mojave (Yosemite and above)

Run these commands in Terminal

sudo ~/Desktop/Yosemite.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled \2 --applicationpath ~/Desktop/Yosemite.app --nointeraction sudo ~/Desktop/ElCapitan.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled \3 --applicationpath ~/Desktop/ElCapitan.app --nointeraction sudo ~/Desktop/Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/Untitled \4 --applicationpath ~/Desktop/Mojave.app --nointeraction 

At this point, your USB should have 4 volumes with different names. Open them to check the installed files.

Install OC

Open Terminal and mount your USB EFI, then copy your working OC to that EFI volume and that USB is ready!

Bonus

How about a multi-installer OS X and Windows? (Windows 8.1 and above)

• You need both OS X and Windows machine
• On Windows -> extract the .iso to a folder -> rename the folder to WIN -> install Partition Wizard -> format your desired volume in NTFS format
• On OS X -> install Paragon Microsoft NTFS -> open windows disk and copy everything INSIDE the WIN folder to the USB. You're done now!

NOTE: You should install Windows in the last volume of the USB