verbs - Is there any other way you can "wax" as you do when you "wax philosophical"?

As I understand it, to wax means to grow: if you wax philosophical, you grow philosophical, which probably means you become philosophically-minded, at least for the moment, and you occupy yourself with philosophical thoughts.

This is the same construction as when you grow old: old and philosophical are best considered subject complements, which is why they are adjectives, not adverbs.

[Edited:]
According to Etymonline.com, both come from the Proto-Germanic verb *wakhsan, "to increase, grow", which in turn comes from Proto-Indo-European *wegs-, an extended form of the base *aug-, "to increase". Other dictionaries render this form as *owegs- or *awegs-. It is related to augment, which has come to us through Latin augeo, "to increase", and to Greek auxô, also "to increase".

However, a Dutch etymological dictionary, De Vries (4rd edition, 1997, p. 819), is undecided about the etymology of the substance wax (Dutch was, which is indisputably cognate) and gives Proto-Germanic *wahsa as a possible origin, related to English weave. The Proto-Indo-European root would then be **weg-/we-, "weave".

The great Woordenboek der Nederlandse Taal (article Was (II) from 1988) mentions both origins and says the matter is still undecided. It notes that Latin cera, the substance wax, comes from the same root as Latin cresco, "to grow", which might support a parallel relation in Proto-Germanic; the substance wax would then be "what grows slowly", as the bees add to it incrementally (yes, increment comes from Latin cresco). Note that the Latin words are no cognates of our word: they come from PIE *ker-, "knead", the origin of our words ceramic (through Greek kerannumi, "to knead") and crescent (through Latin cresco).

However, adds the WNT, modern German has Wabe, "honeycomb", which comes from aforementioned PIE *we-, "weave", and may very well be related to the substance wax; in addition, Dutch sometimes had een(e) was ("a wax", as opposed to simply "wax") well into the 17th century, which might indicate that the word referred to the piece of wax that constitutes a honeycomb.

A German etymological dictionary, Köbler (1995), is very succinct, but appears to consider the PIE root *we- cognate to PIE *wegs-.