It depends on what you ask of it. The whole picture seems too broad for 3 months work. I would approach from a user stand point and ask yourself what this taxonomy would do to be of help to the user? I get easily bored of endless discussions on what pigeon hole to put things in. If all you do is put things in to categories, what value comes out of it. If you have 100 random people and put them in an order by shoe size, it is easy to measure. After you are done with this accurate system, what do you do with it?.
Type is far more complex than shoe size but after you put everything in a category, what do you do with it? Does it matter?
The current taxonomy is very roughly based on history and what came before what. Several years back, this was much easier. Today, where every old face has 10 revivals and knock-offs, it is much tougher. Again, if you do it, what will it do for you for the trouble. If when you finish, all you get is a bunch of argument about the result, what have you gained?

My thoughts as of last year: http://kupferschrift.de/cms/2012/03/on-classifications/

People interested in type taxonomy should know that I am hosting a panel on design taxonomy at the College Art Association Conference in New York City next February. Here's the call for papers (proposals due next Friday!):

PUTTING DESIGN IN BOXES:
THE PROBLEM OF TAXONOMY

When design historians label a chair as “Louis XV” style or a typeface as a “humanist sans-serif,” they are imposing classification schemes upon these design artifacts. This taxonomic approach, which has shaped much of design history, itself deserves attention. This panel welcomes papers that address the problem of taxonomy in the historiography of design, whether through case studies or theoretical reflections. Papers might consider the entrenchment of classification systems in the practice of design studies (e.g., in textbooks and syllabi); might address the roles of industry in both demanding and supplying classification schemes; or might probe the points at which taxonomic systems fail. Looking ahead, papers might also propose new strategies for effective classification (perhaps employing bottom-up semantic tagging in place of top-down fixed categorical schemes). The panel will consider how the intentional examination of the problem of taxonomy can generate insights both about design and about the scholarship thereof.

Proposals due May 4, 2012
Session chair: Craig Eliason, University of St. Thomas (MN)
Participants must be members of the College Art Association at the time of the conference.
More information and forms at http://www.collegeart.org/pdf/2013CallforParticipation.pdf

Can you say more about what you mean by "graphic construction system"?

Each approach has its pros and cons. But we still don't have a good ahistoric/form-based one, so I hope you go for it - you can certainly make some progress in three months (although maybe not enough to pass some kind of formal academic evaluation).

I think the key to avoiding an overwhelming complexity is somehow layering or grouping the various form-based concepts for people to navigate through, as deeply as they feel like.

hhp

Thanks Eliason, it sounds very interesting but I don't think I can have anything on the deadline. This is just a draft idea.

This taxonomy would not be very useful for the end user of typefaces but rather to the people studiyng or designing type. The value of categorization is that it enables systematic analysis and eases discussion.

By graphic construction systems I try to point out the different graphic techniques or styles that can be used to create letterforms. Each technique has an inner logic that will manifest in the final letter shape. The central problem would be to create a vocabulary to describe very abstract categories such as different stroke modulation styles in sans serifs. Other categories would be easy do describe when they follow primitive graphic principles.

Maybe it was too soon to post the idea, I'm having troubles to come up with appropriate categories for fonts like Neo Sans or Cholla Sans.