You can I believe; it's a QA-test install I perform at least weekly with Lubuntu (it's a QA testcase for them).
It's called "Install using existing partition" in the Lubuntu testcases; but this type of install works with all flavor and I use it myself with Ubuntu-MATE on occasion too. See https://discourse.lubuntu.me/t/testing-checklist-understanding-the-testcases/2743 and search for "Install using existing partition" for what I've written there; where you'll note I refer to non-standard packages (clementine or a music player) & some music as examples of packages QA-testers can look for.
You perform the following steps
- backup all data (it's easy to make a mistake)
- boot the media you want to install
- start
ubiquity installer
- select existing partition(s) but ensure you do NOT have format ticked for any
This will cause
- installer will note your manually installed packages
- erase system directories
- install the new system
- if internet is available install the extra packages noted earlier (you need internet available!)
- ask to reboot (and won’t touch any user files unless you formatted)
This type of install is triggered by the lack of format.
It works with Ubuntu repository software; sorry in QA-testing only Ubuntu repository software is used, so I have little experience with it on 3rd party software. Personally I remove all 3rd party sources prior to using this install so it works cleanly if it's my own box; and add the 3rd party myself later.
It also allows you to change release; ie. I used this install because I was lazy & just upgraded 18.04 systems to 20.04 without using do-release-upgrade as it takes a fraction of the time & has the ~same result (sure metadata shows I re-installed; but the effect to me is identical! if I ignore datestamps on files & contents of history etc).
I only pass the QA-test installs WHERE packages installed prior (and I'm talking about pre-installed non-default packages from Ubuntu repositories) get re-installed. It's worked on all releases of Ubuntu-MATE (for other releases I've used it back to Ubuntu 11.04 if not further back)
ps: for at least one of my 18.04 to 20.04 installs; I'd used encrypted-partition which was a default on the initial install (maybe 17.10) but is no longer offered by default. For that machine I had to add a package during the live session before I started the installer (ubiquity) to ensure the system knew how to handle the encrypted partition, but outside of that apt install it was the same.
