First off, once the Philosopher discovers Shirou lacks the Emiya Crest fragment Kiritsugu had, is there any possibility he could retrieve it from Kiritsugu's body? I mean, was he cremated or what, and if so, could the author handwave-change it having been buried, and not having decomposed or dispersed or whatever to leave the Crest intact enough for transplanting?
On to the argument about Crests and their capabilities...
I'm basing my arguments off of the current <a href='http://typemoon.wikia.com/wiki/Thaumaturgical_Crest' target='_blank' rel='nofollow'>Type-Moon Wiki article</a>, so bear with me.
To start, a Crest is a conglomeration of multiple Circuits altered, forged, and preserved into a single meta-physical/mystical organism/item/organ. Quite different from untrained/unused Circuits harvested off of individuals and transplanted, one-by-one, into someone equally untrained.
The article states that a sufficiently stable and properly integrated Crest allows its user to cast any spell stored within it, irregardless of their having learned it. Channel energy into the Crest, find the spell, activate it with the Incantation and Thaumaturgical Process, use the spell.
I haven't found thaumaturgical process as a distinct article, rather something repeatedly mentioned. Likewise, I wasn't able to find something clearly stating, one-way or another, how Elemental Affinity restricted or enabled spellcasting.
I get the impression, however, that it's possible to learn and/or perform various spells with a specific elemental connection, irregardless or personal Element. It's just really, really, really difficult, so as to be effectively impossible, or at least extremely impractical, to be proficient in magical processes or abilities, which would allow mages to create new spells, or modify existing ones, or perform complex non-spell works of magecraft related to a specific element.
This would mean, however, that it's possible to perform spells in a rote fashion, and more importantly to the discussion, it would allow a magi to cast a spell they aren't elementally aligned with just by channeling power into their Crest and repeating a standard incantation. They wouldn't, however, be able to use the more impressive benefits of the Crest, which is an accumulation of theoretical knowledge, experience, skill, and practiced capability, allowing successive generations of magi to skip years or decades of practice at the basic and intermediate levels of a magical field, and instead use their lifespans to further advance their families understanding of whatever goal of field of research they're focused on, eventually allowing a successive descendant to achieve a pinnacle work in their own lifetime.
I specifically believe this based upon my understanding of Emiya Kiritsugu's Innate Time Control. A very complicated application of magecraft towards a specific goal, based upon his family's research into time manipulation, which he is capable of despite having only a portion of the Emiya Family Crest. The combination of his familial affinity, and the knowledge and aptitude they gained from their research for four or five generations (Kiritsugu's father being the Fourth Head of the family) which remained in their Crest, however fragmented Kiritsugu's inherited portion actually was, allowed him to create a complex specific ability/spell that his ancestors hadn't actually encoded into the Crest.
A random Magus receiving another family's Crest, however, wouldn't have the inherited (possibly bred for) affinity and aptitude towards the more complex family research, allowing them to merely reproduce existing spells, rather then applying concepts, ability, and understanding developed by others to create new spells and further understanding, or rather levels of capability, for a subsequent generation to inherit. They'd be able to access the research, but they wouldn't be capable of completely understanding, continuing, or directly applying it, making it almost worthless fr them except as a starting point to reshape their own families goals and start from a slightly better-informed scratch.
So.
To back away from my explanatory soapbox, and get to how this would effect the existing argument, I believe that a Thaumaturgical Crest would allow a magi to cast spells stored within the Crest, regardless of their affinity. They wouldn't, however, gain a new affinity, or have a significant edge on learning new spells they aren't naturally inclined towards being able to use.
Transplanted general Circuits, which were the point of the OP, wouldn't carry any affinity either. More importantly, they would hold no spells, understanding or capability to grant the magi, merely being additional channels for power and spells the magi would have to supply themselves.
As I understand it, Circuits channel Prana, rather then generating or storing it, so this would not actually increase a Magi's power so much as increasing their ability to channel and use it.
Further, since it is already possible to artificially transfer circuits from magi to magi, it's unlikely that this Philosopher would be researching how to do that.
Rather, I'd assume he/she/it would be attempting to come up with a way of allowing safe transplantation between naturally incompatible magi. Like how organ transplants could theoretically be conducted by using immunosupressants to adapt an organ to a different bodytype, and vice versa (P.S. not a doctor, no idea if this is valid or wrong or already in practice rather then theoretical, or what). A way of preventing the body from reacting negatively and rejecting the new circuit, but rather integrate and become capable of fully using it.
Or, given that number of Circuits is less important then the quality and precision of the Circuits (see the Aozaki and Barthomeloi bloodlines), this Philosopher could be looking to come up with a way of switching low-quality Circuits for more capable ones, to produce one superior magi at the expense of several others who had better circuits.
Or use the circuits of other (donor) magi to artificially strengthen and improve the existing circuits of a recipient magi, thus allowing them to be more capable then they could otherwise possibly be.
Or something else.
Anyway, hope something I've typed helps resolve the argument, or improve the story this idea could become, or both.