Was wondering if it was possible, as surely you’d have to write multiple images to the same SD
I think easiest way to have multi oses on same SD card is using NOOBS
But I myself prefear one SD card for each OS I play with.
Grab raspbian desktop as the mycroft-core is very easy to install.
Follow Getting Started
Its very easy and the community will help you with startup and a few tweaks
You migh even want to have a look at https://dot.kde.org/2020/03/26/plasma-tv-presenting-plasma-bigscreen
But haven’t played yet.
It is true what @StuartIanNaylor write - that is a way to go, but I understood that you wanted to have different images like OSMC.tv to have a great media center, and then boot the Pi and have a full blown desktop, and then boot and have a Mycroft device, and then boot and have a nother linux distribution dooing something else.
That is why I pointed at NOOBS. But If you want to have everything at same time go like @StuartIanNaylor says - install raspbian desktop and then Mycroft-core and what else you want to use.
Just notise that Mycroft-core do need som ressourceses so I recomend the bigest Pi4 to have desktop and mycroft at same time.