I had updated my Mac from Ventura to Sonoma beta 7, and now want to have also the Ventura on my Mac. Below is my process. The problem was that I could not select the volume where I wanted the Ventura.
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I downloaded the "InstallAssistant.pkg" for Ventura and extracted from it "Install macOS Ventura.app". But it could not be started, because I was using macOS Sonoma.
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I made an apfs volume where I want the Ventura installed. On ssd, there are also other volumes
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Then, following guide of Apple (HT201372), I made successfully a bootable memory stick.
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I closed the Mac, and booted it keeping the start-button pressed
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I selected the just made external volume, and it was booted
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The start page of install app did not come up, but followed a series of boots with text (with estimated time) on black background
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Finally Ventura was installed, and dual boot (Ventura / Sonoma) working
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The final result was ok, and Ventura was luckily not installed on my document apfs volume, but on one of the two empty apfs volumes I had.
Before this all, I had a working Ventura, and I wanted to have Sonoma beta 7 beside it. But the update process which started from System Setting, replaced my Ventura by Sonoma beta.
It is a bad idea, if Apple is dropping informative details in these install processes.