O.K. now that I have scared you to death with all the problems that can arise, I would like to now explain how you can avoid them and how hypereutectoid steels can be our friend and very useful for the right type of knives.
First of all, it should be readily apparent that if one wants to work with hypereutectoid steel they really need good temperature control for total success. If you do not have the tools or skill for this level of control, a eutectoid like1080 or 1084 is a much better choice.
Now what to do with that pesky extra carbon? Obviously we do not want it in the grain boundaries, or of we have alloying we dont want it making big lunky carbides within the grains either. To avoid this we just have to watch how we cool it from solution, we need to deprive it of the time needed for it to get into mischief. Slow cooling from high temps give it this time, so when working with hypereutectoid you need to forget all those annealing operations that involve wood ash, vermiculite, or stuffing it in forge for the night. Going any slower than a steady air cooling could give you problems, but if it is enough to beat the curve you can trick that extra carbon into sticking around and forming wider carbide bands in the pearlite or many finer alloy carbides. So for these steels normalizing and spheroidal type annealing are what you should stick with. Once you put that carbon in good places, keep it there by staying below non-magnetic in other heating operations until you are ready to harden.
When you harden you have to keep your temperatures lower than with a eutectoid. Ever wonder why the recommended temperature for 1095 is often given at around 1475F but 1084 can be higher at around 1500F? It is because 1084 can take it, because it doesnt have that extra carbon to cause problems. The recommend temperatures that bladesmiths love to ignore or ridicule because those irrelevant eggheads in industry came up with them were developed through an awful lot of study on exactly what temperature will put just enough carbon into solution to get maximum hardness and leave the rest in the from of very nicely distributed fine carbides to aid in resisting wear.
So when you have a steel well above .8% carbon be certain to normalize well without overly slow cooling, use sub critical anneals by cycling above 1100F but below non-magnetic (not only will the steel love you, your mills and drills will as well), and be careful to keep the temperatures below Accm in hardening. Unfortunately the best way to accomplish that last one is to have a well calibrated heat source. Lower temperatures and longer soaks are much better for hypereutectoid steels.
Many bladesmiths love to use complex steels and then inflate all the ins and outs into a huge mystery they have some special insight into, like the world wont truly understand these alloys until they blaze the trail with their silly fumbling. These steels were made to do specific tasks and are understood quite well by rest of the industrialized world. Many of these mysteries are simply created by smiths unnecessarily complicating matters by blindly stabbing at answers with inadequate knowledge or tools, with knowledge being the most important tool. Many feel their position as a smith relies upon there being a big mystery around these things, so they scoff at this information as being irrelevant, overly technical or perhaps even robbing bladesmithing of its romance and tradition. But isnt it nice how easily things can be recognized and dealt with by anybody armed with a few facts.