Amusingly, this was something we covered when we were making the nagas mod...
(Image not mine, and I didn't actually go with that exact layout.)
Somewhat similar to the previous description given by JesterHell, multiple hearts and a secondary lung are needed. It's worth noting that even
normal, real-life snakes need a secondary heart.
One of the things I changed, however, was the position of some organs, including having kidneys and bladder in the "human part"/upper half. Bladders only need to be near the kidneys, and it's only for the convenience of only needing one hole in the rear that a cloaca would develop, so if you want to spread organs out, you can. I'm no biologist, but having the kidneys closer to the main heart and lungs and areas of most blood flow has a good chance of being biologically useful. (Putting reproductive organs on the human parts also helps avoid some "beastiality" claims from what TVTropes calls
The Mermaid Problem.)
Dwarf Fortress can make things easier because the tissue templates already scale organs to the overall size of the body and to certain body parts (although this can have negative impacts in some regards, as small parts like fingers have thinner skin than large parts like torsos, as thickness is based upon total width of body parts), so a very large humanoid has proportionally large organs. That said, if you have something like a drider, the human portion's lungs aren't going to be enough, as already mentioned. (And if you take the body plan of a real spider for a drider, then you have tremendous problems, as exoskeletons won't work for a creature of that size, and many spiders have no lungs at all, relying upon airholes in the exoskeleton and the lymph system.)
DF tends not to be realistic with the biologies of its fantasy creatures (hence Bronze Colossus), but if realism is the goal, here, we need to make creatures of different sizes have body plans based upon size more than upon the chimeric creatures they are supposedly made from.
I'd explain in detail, but Kurzgegat did it for me, and with animations. Square-cube law also dictates the thickness bones need to be, as the mass of a creature is cubed as you double all the dimensions of a creature, and yet the bones that support the creature only quadruple in thickness, meaning that twice as much strain is placed on the bones. Those thick, tree trunk-like legs of an elephant are basically all bone, and from there, if you somehow want to make an even larger creature, there is nothing you can do besides make the bones even more ridiculously thick.
What this means in practical terms is that it might work best to do like the procedural demons - start with a size, then have some optional parts that can mix-and-match to add variety. Hence, if we have a system where we presume the split between one animal and another takes place at the divide between upper and lower torso, you just presume all functions of a certain kind (like having heart and lungs) are taken care of by the upper torso, while if a lower body has special needs (like a very long snake-like body needing a secondary heart), that can be added in by that particular lower torso. You might have special biped versions or quad- or octo-ped versions of the same types, and have descriptions that just say this quadruped is more like a tiger and that one is more like a horse. The upper torso might have different numbers of arms or added wings, but have a set number of functions it has to perform like have a heart or have an excuse for not having a heart (like being living stone), instead. (Granted, this can also result in a horse-taur that has the head of a horse and the lower body of a horse... yet still have a human torso upper body.)
That said, one thing to keep in mind is that I don't think that DF cares about organ sizes right now in any way other than how easy it is to hit them. Dwarves have larger livers in DF as a half-joke for all the alcohol they consume, but most organs don't have a function tied to their size, and many organs lack any function at all. (Spleens can be torn out with impunity, for example, nevermind having a small one having no impact. In fact, years ago, I remember that your heart being damaged would only kill you from blood loss, not cardiac arrest. I don't know if this has been changed by now. Hence, having an organ too small for your body is almost certainly not something DF considers when assessing the health of creatures.)
Also, one thing I think is worth keeping in mind is that legends of the unicorn aren't just horses with spiral horns like popular culture shows them today. They had a body of a horse, a tail like a donkey, feet like an elephant, and a curved horn. Some scholars think this was actually referring to the rhinoceros, and people just used descriptors of parts being shaped like other animals to paint a picture of overall body shapes before some people started treating it like it was a chimera. Especially if we're going for a more realistic "evolved" (rather than magical Frankensteining done by the gods) tauric creature, simply slapping parts from random creatures together makes a lot less sense than just having new creatures that have parts that copy the same function or vague shape of other animals' body parts, but if one part is a zebra, and another part is like a gorilla, it makes more sense to either have stripes throughout the whole body or no stripes at all, as partial stripes isn't as advantageous.