Before I begin, what I mean by 'systems' is what I've dubbed 'axiomatic systems', those which act as the starting point for all knowledge, for which I know of three: Maths, Logic, and Set Theory. I'll just call them systems from now on, though.
I'll first begin with my intuitions behind this question. Most of you here will be familiar with logic, being that it's the 'tools of Philosophy'. Whenever you do logic, you're working within a system. One can't just 'do' logic, for logic is the activity within the structure of a system. So the reason you can't just do logic is for the same reason you can't drive without a car.
So, such systems have to be literally designed; its axioms must be discovered, it's properties must be studied, its values and operations must be declared before use, etc.
I've been looking for this answer for quite a while, and in searching the depths of the internet the best I can find are papers that partially (and very briefly) study some of the aspects of the analysis and creation of systems. What I really want, however, is an academic, and rigorous field of study that gives an exhaustive account of how such systems are created. I think the reason why am having trouble is because am using 'systems' in a very technical way, and I have no other way to really express what I mean other than "systems".
Quick note: There are fields out there looking at the use of systems (maths, logic, set theory), how they can be combined, how there used in computer programming, but none which seems to study the actual systems themselves.
Oh, by the way, am not sure what to tag this as, so sorry if I've missused the tags I have provided.