Hi Happy Girl,
The answer is a very unhelpful both.
Everyone has transference in every relationship they have in that we carry an internal relationship template, with expectations based on our early childhood relationships with our caregivers. This forms our expectations and beliefs about how relationships work and we bring it to every relationship we are in. The ones that are particularly intense are usually someone who is a closer "fit" to our template, they "feel" right and its easier to connect with them because in some sense you share a basic world view. Or if we were particularly deprived, someone who provides care and concern can activate the longings you still carry about unmet needs. Sometimes its both.
So usually when we have strong feelings about someone that are invoking an intensity from our past, there is, so to speak, a hook to hang it on. But we really are interacting in the here and now with the real person. But our feelings about what they do, and our projections onto them can be highly influenced by our past.
Ts are ripe for this type of reaction for two reasons. One is that while it is a very weird duck, the theraputic relationship is closest to a parental one. Our needs and feelings are the focus. Getting that kind of attention, ESPECIALLY if we didn't get that from our early caregivers can be incredibly powerful and we can respond like a starving dog thrown a steak.
Also, a good T will keep their own feelings, wants and desires out of the room, so in some ways we are free to create the "perfect" person. Therapy is a playspace in which we can choose (unconsciously) to believe what our T is thinking and feeling and let that play out. So often our unconscious wishes, desires, and fears manifest in the therapy relationship.
So basically, if their are deep, unprocessed issues then they can manifest in any relationship, but the theraputic relationship is a setup in which this type of thing can really flourish.
So yes, you could form another intense relationship with your therapist, but in the end, you're more than likely dealing with the same underlying issues, so as you resolved them with your T (who actually is a suitable person to do the work with) it can also clear up the other relationships.
And for me personally, full confession mode, I went into therapy with my second T when I was dealing with a pretty intense "transference" relationship (didn't see it that way until later) and my feelings about that T REPLACED the intense feelings I had with the other person. It probably helped that he had moved away and I didn't see or speak to him as often, but for me, it seems like I only do this with one person at a time. So the good news is that it won't be double the agony. The bad news is that it will probably be the same agony. But the best news is that in therapy, you will finally have a chance to understand and heal.
AG
