The hypothesis of the soul and the soulmate is such that scientific literature fails to validate, so all we have at our disposal is the work of poets and ancient Greek philosophy, which has pondered on the idea of soul and soulmates quite often. In Aristophanes' play "The Symposium" it is written that Plato expanded on the notion of love as it relates to Soulmates:

“Humans were created with four arms, four legs and a head with two faces. Fearing their power, Zeus split them into two separate parts, condemning them to spend their lives in search for other halves. And such a nature is prone to love and ready to return love, always embracing that which is akin to him. And when one of them meets with his other half, the actual half of himself, the pair are lost in an amazement of love and friendship and intimacy, and one will not be out of the other's sight, as I may say, even for a moment: these are the people who pass their whole lives together, and yet they could not explain what they desire of one another. For the intense yearning which each of them has towards the other does not appear to be the desire of lover's intercourse, but of something else which the soul of either evidently desires and cannot tell, and of which she has only a dark and doubtful presentiment."

In other words, Plato's soulmate idea conveys the impression that:

We are a set of predetermined features and psyche markers and
There is only one other being who is an absolute match for us because of their accumulation of reciprocal attributes and character qualities.
Therefore, the goal of finding one's soulmate is to single out this person, and then the assumption is that once this person is found, it will be smooth sailing because the two separated halves have become reunited. In this way, the Aristophanes’ script is primarily a happily-ever-after script. This script surely has a place in Disney stories, but not in real life.

If we may look past the romantic value and observe the absurdities presented in this play, we will see that biggest logical error is Plato’s argument assumes that:

Our character is fixed and static over the course of life, therefore we can spend our life with a similarly static being, whereas,
We may have observed over the course of our individual human experience, that we are dynamic, we change, therefore
The metaphorical one true “other half” has to be equally dynamic and be changing in the same ways for it to retain that position to continue to be our other half, which if not impossible is very unlikely, because

So far I have observed that no two free-wills flow in the same direction.

Realistically, to reach at the true definition of soulmate, we have to look at the concept of soul first, which can be interpreted as the distinguishing factor between living and dead, so we can assume that the essence of our life has found its expression in soul, which to say, is a combination of

Our ever-changing characteristics,
Our perception of different ideals, and
Our dreams.

These three elements sum up the faculty of soul along with an additional dimensionality of existing in a spiritual realm, but since there is no way I can describe or define or comprehend what that is, we are going to restrict our definition of soul to only the aforementioned three elements, and assume that the totality of our existence is the composition of these three attributes.

If we agree to this definition, then a soulmate will essentially be a being who is:

understanding of our desires,
shares a similar perception of different ideals,
and has an empathy towards our ever-changing characteristics,

and this soulmate may or may not be the same person whom we love, since love is the commitment to another person’s overall well-being, which can be applied to multiple people

or the same person whom we end up being physically intimate with, since that is the function of mental receptors being stimulated in a way that finds its expression in ‘being attracted’ or ‘seduced’ and that in turn sometimes depends on something as ephemeral as our physical features, or something a bit more permanent such as intellectual features and again can also be applied to multiple people, but

as you can see, all three of these components of soul are neither mutually exclusive nor mutually inclusive, sometimes we find one person to be our soulmate, lover, and partner, and sometimes the extent of our soulmates can range from blood relatives to strangers we find in foreign places while loving different people and at the same time being physically intimate to a whole another set of people who are immediately available (and attracted) to us depending on geographical proximity.

So yes, it is possible to have more than one soulmate.