I've recently gotten the point in my Japanese studies where I'm beginning to feel confident enough to read things I actually have an interest in reading (at least the easier stuff). So I started reading Muv Luv Supplement, I already knew the characters, and the dialogue is fairly easy, so it seemed like a good candidate.
Muv Luv Supplement contains three parts. "Muv Luv After Story", which is a continuation after Sumika's route from Extra and is the only part I've currently completed. "Muv Luv Duelist" which uses the Rumbling Angel card game alongside characters from Muv Luv to tell a side story. You actually play the card game, and I wasn't confident in learning the rules so it's something I've left to the side for now. My initial experience went something like this:
OH GOD, WHAT DO I DO.
The last part is "Muv-Luv ～Another Episode Collection～"which is a collection of short stories typically featuring one of the heroines. I have not yet played through these, but I'll likely do them sometime in the future. When I do, I may update this for a part 2.
The story takes place after the events of Sumika's route in Extra, but despite this, this story is actually a fairly good end to Extra in general (if we consider that Unlimited/Alternative didn't happen). Despite it taking place in Sumika's route, I wouldn't hesitate to call this the true end to Extra, as it kind of brings closure to everyone as they graduate from Hakuryou. Of course the main focus is on the relationship between Sumika and Takeru. Early on in the story, a dispute between them happens, and the entirety of the route is trying to mend this problem. Of course Extra Takeru isn't exactly that reliable of a person, so many mishaps happen on the way to reconciliation. But through this, Takeru grows just a little bit as a person.
The story isn't some amazing feat that you will remember forever, but it's a nice aside that finishes off one section of Muv Luv. It carries the comedic aspects from Extra but brings with a sense of finality, especially towards the graduation scene. It even kind of made me feel a little bit nostalgic about my own high school graduation.
Overall, if you're a Muv Luv fan, you probably don't need me to tell you that you should try playing it. Especially if you've completed Alternative and kind of have a longing for Extra again. It's not going to be on anybody's top 10 VNs list, but it's a nice story nonetheless.