The first thing that comes to mind is that playing with the soul can attract the attention of powerful entities -- Gods, Demons, Truth -- and they will certainly have reactions to what the witch is trying. They are messing with the Celestial Bureaucracy and that could have Consequences. Meddling with the Soul is going to cost you, and potentially more than just an arm and a sibling. This danger alone might deter the less ambitious.
But reading it through, the whole process itself is laden with pratfalls and traps that have to be navigated through for a successful reincarnation. The trick is to look at what you have and go "Where can this go wrong, O Great Murphy?"
The other big question is how common is this spell? If this ritual is widely disseminated, then the pratfalls are likely known and you will likely see more care taken. Otherwise, experience may be the teacher, the cruel grinning teacher.
Her most recent claim, a young girl named Snow White, is the next host that she will possess.
First, there is the victim. The witch requires not only a physically able and compatible body to take over (mentioned already), but a magically compatible one as well. Has Ms. White been checked over to ensure this level of compatibility?
The premise behind this is that a good number of shows, games, and stories portray magic has having some manner of alignment between people, and it is those alignments that need to be taken into account when transferring to that body. It is certainly possibly to groom an aspiring body to have something acceptably close to your alignment, but depending on the witch's alignment (and spell preferences), this might be a tricky endeavour. Snow White cursing the animals while she sings along with them might be noticed.
This magical compatibility can extend to other magical parameters as well. However other parameters are easy enough to groom for with enough effort and/or time so those tend to be secondary for all but the most immediate emergency reincarnations.
Note to aspiring ritualists: Find the sane ones to take over. Distorted mages are dangerous -- even barely trained ones. No matter how tempting the target, Do Not Engage.
Next, I would assume that the victim would need to be prepared in some way. Perhaps this does not need to be an elaborate or expensive preparation, but it is an extra step. While not vital to the process, this step allows the whole process to run smoother and permit a higher chance of success (or lower chance of side effects) than not doing it. Jealous witches may guard this secret step knowing that this is their secret to success, limiting its propagation out into the general magic knowledge.
The limitation here can be that once a body is prepared for the transference ritual, the process has started and a different body can't be chosen until the process is complete or aborted. The pause between this step and the next one can be indefinite, but it needs to continue.
After a person dies, their soul jumps into a magical item called a soul stone, which keeps the soul in storage and prevents it from crossing over to the next world.
The Stone for the Soul
First, the stone. The obvious limitation is that the soul stone needs to be of impeccable quality. The more flawless the stone, the more flawless the soul storage is. Here is where the lossy storage starts to really happen -- only a perfect gem can house a soul without consequence, and if the gem is rendered unusable for a second ritual then sourcing the gem is a definite limiting factor. The more one looks for that flawless gem, the more questions might be raised.
The witch's vanity may also be a limiting factor. Either through bad information, deliberate sabotage by another witch, or simply their own vanity, they have decided that a diamond is their soul stone. It may very well be that an amethyst, quartz, or other lower value and/or more common gem would not only be easier to source for the needed quality, but actually be more compatible with the witch. This leads to the first point regarding quality of the storage medium.
A third limit might be the preparation of the stone itself. Arcane rituals might need to simmer for weeks, months, or even years before the stone is properly ready to house a soul. Said rituals might not need a lot of personal time, but they do still need to happen.
The Soul in the Stone
The first obvious limit is that the caster needs to die. But what is the stone's effective range? If a witch's soul stone is safely ensconced in their laboratory and they are killed kilometers away trying to deal with the pesky interlopers, will the stone still trap her soul?
The next question is how dead is dead? While the question might seem redundant, is a vegetative +coma enough to trigger the transfer? Is being mostly dead but not quite dead enough dead to be considered dead? I could see the same enchanted coma that works to preserve the victims actually preventing the ritual from happening if used on the witch.
Third, how close does the stone need to be to transfer into the new host and how long does one have to do the actual transfer of souls?
The soul is then transported and absorbed into the host body, giving the person possession over it
The result is that the body now contains two souls within it that continue to remain separate, with the original soul remaining trapped and the dominant soul of the witch retaining control.
Possession is Nine-Tenths of the Spell
The Possession part is the biggest pratfall -- You are an invader and your prospective host wants you out. The combat might be brief, it might be protracted, but it happens and is the heart of the ritual. This is the crucial winner-take-all part of the spell and why you are here. The witch has the advantage in preparation but the victim has home-field advantage. The winner gets the body and the loser gets locked away until the chance to strike again occurs. Obviously the witch will metaphorically stack the deck in her favour for this part, but natural talent in this area can't be underestimated.
This might not even be a conscious act by the victim -- See the immune system for why we don't just allow any old foreign thing into our bodies.
The Perils of Winning
So now you have a new (hopefully) younger body, and another lifetime to plan. Well there was one little problem that you only realized as you started exploding. You, the soul of the witch, might be able to channel vast amounts of arcane awesomeness but the young person you just bodyjacked can't. You who are so used to channeling so much power will literally overload your new body's capacity and cause a catastrophic physical failure due to this.
To put it simply, your mind and soul might know how to channel a metric Gandalf-ton of power, but the body you are not in certainly can't handle it and has never been trained to do it since that training would make your victim a threat.
Likewise the opposite might hold -- you can't channel that much, and now the body your in draws in and handles several times what you are capable of wielding safely. All the magic that the body has to go somewhere but you can't actually handle the task of using it. This is almost certainly going to ... interesting.
Other magical side effects are likely possible leading to a trope of the newly reincarnated sequestering themselves in their layer for a time to acclimatize themselves to their new body. Ultimately this is derived from finding a magically compatible host, mentioned above.
So you want to reincarnate again ... great! One problem ... two souls in one body. While in theory, one soul is dominant while the other submissive, but how true is that really? Can a second soul gem only grab the witch's soul? Again, this is where your equal strength qualifier comes in -- Souls holding equal power are actually better able to hold their individuality. This might seem counterintuitive at first glance but consider that if one is vastly more powerful than the other, the powerful ego will either crush the lesser one leaving soul rubble to clean up and maybe attract bad attention, or draw the lesser ego/soul into itself thus muddying the original soul and causing complications further down the line.
The victim and the gem itself appear to be your two biggest pinch points for a successful reincarnation. Unless everything has to be absolutely perfect for the spell to work at all, then I would think that it becomes a case of weighing the options and trying it when they are ready.
Also don't worry if they didn't do a perfect job, failure is always an option. In this case, it can lead to interesting consequences if that is a direction you want to go.
Final Note: It would be ill advised to kidnap Ms. White for this kind of thing as her great-grandmother Betty is older, wiser, better with animals and has spent years being old and powerful without reincarnating.