Since I posted my HDG X Mutineer's Moon crossover idea, I guess I might as well post one or two of the other couple of HDG crossover ideas I've mentally played with (@aloeveracious).
One of them is "what if a human in the Terran Accord was exposed to active tree of life and became a Protector shortly before the Affini started conquering the Accord?" So HDG X Larry Niven's Known Space, or rather specifically HDG X Protector.
It would be a fusion crossover, set in a version of HDG where the Pak planet exists, Earth is a Pak lost colony as in Known Space, and thus Phssthpok arrives in Accord space maybe ten years before the Accord/Compact war.
Phssthpok encounters a human leftist guerilla (after a failed mission, she's hiding out in deep space in a singleship until the heat in the Accord dies down). I'll call her Brin, which sounds a little bit like Brennan so it's a bit of a winking reference. Brin is a childless woman in her forties (so, right age for Protectorization, and will be a childless Protector).
Brin's encounter with Phssthpok goes about the way Brennan's did in Protector. Phssthpok exposes Brin to tree of life, which Protectorizes her. Brin awakens as a childless Protector and adopts promoting human flourishing as the cause that keeps her eating. Brin then has the same post-Protectorization revelation about how dangerous Phssthpok is to humanity that Brennan did and kills Phssthpok with a surprise attack.
Brin then encounters an Affini scout who was reconnoitering Accord systems and noticed the drive plume of Phssthpok's ramjet and decided to investigate it. Five minutes of conversation with the Affini is enough for Brin to realize the danger she's in (Affini aren't exactly subtle about their motivations). The Affini has a much more capable ship, but the Affini is also arrogant in the way Affini tend to be, and Brin is smarter than the Affini. Brin lures the Affini into a vulnerable position, kills the Affini, and thus captures an Affini scout ship. From there, it's a relatively simple matter for her to access the Affini overnet. Just browsing the civilian overnet is enough to tell her a lot about the Compact's resources and capabilities and the Affini's usual approach to non-Affini sapients, and before very long Brin has managed to hack in to private feral control force communication networks and is reading Affini conquest plans for the Accord. Brin's cause that keeps her eating is sufficiently inflected by the values she had when she was a human that she quickly decides the Affini are a huge threat to human flourishing as she defines it and incorporates preventing Affini conquest of humanity as a high-priority subgoal of the cause that keeps her eating (she considers the Affini a sufficiently big and urgent problem that dealing with them firmly bumps "overthrow the Accord's shitty government and replace it with something better" and "deal with the Pak who might be following dozens to thousands of light years behind Phssthpok" into being secondary priorities).
By the time the Affini make their move on the Accord, Brin has managed to upgrade the Cosmic Navy to approximate pound for pound equality with the Affini feral control forces (a Brin-upgraded Cosmic Navy battleship would have pretty good odds of winning a one on one fight against the Actaea). This by itself wouldn't be enough to save the Accord (the Affini still have vastly more resources), but it puts the Terrans in a much better position than they were in the original timeline.
Ultimately, Brin is able to save humanity from conquest by blackmail (same basic strategy I suggested Emperor Colin would use to save the Fifth Imperium in the short term):
1) Brin manages to locate the (still functional) Thrint Suicide Night device and threatens to activate it if the Affini continue their conquest of Terran worlds (yes, the Thrint empire existed in this version of the setting). Brin's Protector instincts would not allow her to actually activate the Suicide Night device (because that would kill all of humanity along with all other sentient life in the Local Group), but she gambles that she can bluff the Affini into backing down.
2) Brin also threatens to inform the Pak that the Affini are coming and provide the Pak with compilers, "FTL," and other technology that would make the Pak an absolute nightmare for the rest of the galaxy. Brin presents this threat to the Affini as an intermediate stage of escalation short of activating the Suicide Night device, but actually carrying through on this threat is actually Brin's back-up plan if the Affini call her bluff on the Suicide Night device. Giving warning about the Affini and tech to the Pak is a sufficiently doesn't inevitably turbofuck humanity action that Brin could do this; this threat is not a bluff.
In the longer term, Brin's anti-Compact strategy will be similar to the one I think Emperor Colin would follow; to form an anti-Affini containment alliance with other sapient species staring down the barrel of imminent conquest by the Affini (Pak Protectors might be too xenophobic to cooperate with non-Pak sapients this way, but human Protectors are better team players than Pak Protectors; Brin's instincts are flexible enough for her to cooperate with non-human sapients).
TBH this is my less "thematic/ideas" HDG crossover idea, I mostly like it as a self-indulgent exercise in playing with the idea of the Affini getting a nasty surprise when they attack humanity, but I guess between this and my HDG X Mutineer's Moon crossover idea you can see a theme forming that if you try to help people in a way that involves radically disempowering them and forcing unwanted "help" on them and do that from a position of great but not completely overwhelming power they're likely to react to that in pretty destructive and self-destructive ways (and might be game theoretically rational in doing so!) and the main reason this doesn't bite the Affini in HDG proper is canon HDG arranges a situation where Affini mostly don't have to take non-Affini very seriously as agents. It's an accidental theme that emerged without being deliberately planned from the incentive landscape of trying to fight the Affini while having less starting resources than them, which I think in a way makes it a pretty neat kind of theme!
Aside: this is making me wonder how the Affini would do against the Thrint empire at the height of its power. It would have a certain metatextual resonance, cause the Thrint are obviously an example of one of the conventional sci fi baddie archetypes HDG is riffing off; a Known Space Human, Puppeteer, or Kzin would probably take one look at the Affini and the Compact and think "Oh shit, Thrint but smarter, hornier, more insidious, and with a less effective bargain basement version of the Power! Oh shit, we just ran into a modern equivalent of the Thrint slaver empire at the height of its power!" Affini vs. Thrint would definitely be a conflict in which Affini would get to be the relative side of good or at least less evil, if the behavior of Kzanol and Dnivtopun is representative Thrint treated their slaves like shit.