A word for "to make more concrete" in philosophical context?

I think that the phrase make more concrete is perfectly acceptable. You shouldn't worry too much about repetition if the word or phrase is correct in the context.

But since you're looking for more options:

• Crystallise - make free from confusion or ambiguity; make clear; — The Free Dictionary

• Make (more) tangible where tangible means able to be touched.

• Elucidate - to make clear or plain, especially by explanation; clarify. — The Free Dictionary

• Materialise - come into being; become reality. — The Free Dictionary

Also consider reify, "to regard something abstract as if it were a concrete material thing", with synonyms conceptualize, concretize, objectify, picture. Related term reification means "consideration of an abstract thing as if it were concrete, or of an inanimate object as if it were living". From these definitions one sees that reify and reification refer not to making something concrete, but instead to regarding it as if it were, which in your philosophical context may be suitable.

Edit 1. I wrote "consider reify" above, rather than "use reify", due to not finding meaning in the example sentence, hence not knowing what part of speech to suggest. The comment "Objectify fits nicely" suggests to me that objective [which is analogous to pragmatic, from another answer] may be relevant. Perhaps the example means something along the lines of

Applying X philosophical ideas to reify Y issues makes these issues subject to objective scrutiny, but also requires philosophical machinery Z to do A to B.

Edit 2. From etymonline, reify has a Latin stem, re, with English suffix -ify attached; if you require pure English, substitute thingify for reify. The etymology of reification makes more interesting reading. From etymonline and wiktionary, respectively, we have:

1846, "act of materializing," from L. re-, stem of res "thing" + -fication. In Marxist jargon, translating Ger. Verdinglichung.

c. 1846 Macaronic calque translation of German Verdinglichung, using -ification (“making”) for ver- + Latin res (“thing”) for Dinglichung (“thingliness”)