Uriah Kriegel has a very nice manuscript, Sketch for a Theory of the History of Philosophy ("just for fun...", he says on his own website). Kriegel suggests four stages in theorizing with respect to the history of philosophy;
(1) Singular Causation: This stage obviously deals with influences between thinkers and the like.
(2) Processes: When we take singular causal links and chain them together, we get processes. In historiography of philosophy, this is associated with the study of changes in movements and schools; Kriegel gives as examples studies of the evolution of scholastic metaphysics from Aquinas, of the evolution of German Idealism from Kant to Hegel, and of the evolution of analytic philosophy from the early days of Frege, Moore, and Russell to its later days.
(3) Causal Laws: Causal laws take causal links and categorize them so that we are no longer talking about the relationships between tokens but the relationships between types. Kriegel suggests that this has largely vanished from philosophical discussion.
(4) Total Theory: This considers the history of philosophy as a unified and coherent whole; Hegel is the most famous example of an attempt at this. This, Kriegel suggests, has also largely vanished.
While I think it's true that (3) and (4) have largely vanished from explicit discussion by philosophers, I think this is more symptomatic of a crisis in the understanding of what philosophy is than anything to do with history of philosophy as such. That is to say, your positions on (3) and (4), and how to go about them (if at all), will primarily derive not from any historical facts but from your account of what philosophy is. The total theory of Hegelianism or Absolute Idealism or Marxism falls out of how philosophy is understood in these approaches. If you think of philosophy as just a sort of hunting for and systematic exploration of solutions for problems, you will get another implied total theory; if you think of it as proto-science, you'll get another implied total theory; and so forth. The lack of any explicit discussion of total theory has a great deal to do, I think, with the failure of modern philosophers to grapple properly with the nature of philosophy itself -- and in particular with the extent to which they disagree on that very subject, and perhaps even fail themselves to have a consistent view of it.
But in practice, if you look at discussions of processes and even singular causal links, there clearly are assumptions being made about the domain of (3) and even (4); people will assume that philosophy has no particular directionality, or that secularization arises naturally from arguments over ideas (rather than, as one might well hold on the basis of other historical evidence, from political classes using political power to marginalize religious influences that can interfere with them), or that extensive theorizing eventually leads to overtheorizing and that to reaction, or that eclectic approaches through intense argument morph into systematic approaches, or that systems with a lot of ad hoc additions tend to 'break down' in the sense that they become too costly to hold, and so forth. These aren't systematic, but things like these are there, assumed and sometimes even loosely argued for. And something like them has to be there. We don't, even in everyday life, always start with singular causal links and then get processes and then get classifications of processes and their parts; we often have a vague sense of the whole context and we analyze down to understand the singular causal links in that vaguely conceived context. Thus, while purely textual analysis of (say) Malebranche's influence on Berkeley is done, most discussion of it is in context of a general sense of disputes between rationalists and empiricists (in which assumed context rationalist Malebranche being such a direct and important influence on empiricist Berkeley is a boundary-crossing case in need of special clarification, which is the sort of thing a graduate student might study for a dissertation).
Part of this shows up in periodization, which Kriegel discusses. It is, of course, commonplace that the standard Ancient-Medieval-Modern periodization is absurd; 'Medieval', as its name implies, is very obviously just a miscellaneous period for whatever happened between the Ancient and the Modern periods; as Kriegel notes, we largely use this periodization as a sort of relic of the German Enlightenment. Regardless of source, this approach to periodization -- now almost unavoidable given the way academic philosophy has built itself around it -- regularly sidelines important figures and makes divides at the boundaries seem sharper than they already are. The source, however, is relevant, because in fact the periodization comes from 'total theory' assumptions about universal history.
Kriegel proposes a parallel-streams total theory, which he suggests is "the most banal and undaring theory of the history of philosophy one might come up with" (p. 9). I don't think this is an accurate description at all -- it is neither banal nor undaring, and I think, with respect to what I have previously said, that it requires a rather schizophrenic understanding of what philosophy is, since its implied characterization of philosophy is as a very simple oppositional dialectic. But in any case, Kriegel imagines two 'temperaments'. Temperament A is inclined to be favorable to abstracta, necessities, a priori cognition, monism, literary presentation; Temperament B is inclined to be favorable to eliminating these things. It seems clear that these are not 'temperaments' at all; despite nominalists giving themselves airs, nobody actually has a temperamental inclination to Platonic heavens or desert landscapes, and the Coleridgean notion that everyone is either a born Platonist or a born Aristotelian depends on a rather robust total theory of dialectic, not facts of psychology. Rather, these are stances that end up being loose commitments given other things that are accepted. And the things that are jumbled together on each side are only related relative to these kinds of background assumptions; that is to say, how related they are to each other just depends. Even allowing for idealization and simplification, Aristotle looks Temperament B only if you compare him to Plato; he perhaps looks Temperament A if you compare him to Hume, although Hume is in reality much more obsessed with literature-style presentation than most people who would naturally be put under Temperament A. And nothing really rules out taking what might be called the Neoplatonist view and regarding Plato and Aristotle as effectively sharing the same temperament (Temperament A), just discussing somewhat different fields.
(Kriegel, I think, overstates the evidence of the history of philosophy in his favor on this point; his characterization of most of history up through the Renaissance as Plato vs. Aristotle is largely an artifact of the Renaissance rediscovery of multiple Platonisms and the humanist back-to-the-sources approach. For most of the thousand years before that, most thinkers saw Plato and Aristotle as largely the same, with some difference of emphases and maybe some un-explain-away-able disagreement on an issue or two; there were hyper-Platonists and hyper-Aristotelians here and there, but they were by no means the dominant views. Bonaventure is more Platonist than Aquinas, explicitly agreeing here and there with Plato against Aristotle, and Aquinas more Aristotelian than Bonaventure, but they both saw Platonism and Aristotelianism as largely of a kind, and both can be categorized as either, depending on what you look at.)
In any case, Kriegel suggests that within a given stream (A or B), change is a result of three tendencies: influence of similar earlier thinkers, counter-influence by thinkers of opposing temperament, and individual motivations and dispositions. We then take major figures to be those who show much clearer individualization and much more extensive influence and counter-influence on others, which I think is certainly true of what has usually been actual practice, although I think this can be said independently of any posited temperaments or streams. As Kriegel notes, thinking of things this way suggests that we should periodize not by times but by phases within streams (which will not be wholly independent of what is going on in the other stream, due to influence and counter-influence); it's very interesting to think about how this sort of multi-stream periodization would work, on which he makes some other interesting comments.
These things are always interesting to think about. In a similar 'just for fun' vein, I did some thinking a number of years ago about how you might give a simplified but reasonably accurate approach to the dynamics of long-term philosophical interaction if you were attempting to simulate it in a history-of-philosophy strategy video game:
Some Thoughts Toward a Philosophy Video Game
Obviously there are concessions purely to the requirements of such a game, and simplifications for approximate effects, but I put a lot of thought into the HoP background, and it's worth contrasting with Kriegel's suggested theory; the one I posited is not stable dual streams in parallel but partly randomized crisscrossed multiple streams, it is not strictly dialectical, and it depends as much on external institutions as on internal dynamics and influence. The last of the three points is, I think, particularly noteworthy; analytic philosophy or phenomenology, for instance, would not survive for long, at least in anything like their current forms, outside the modern university, which effectively subsidizes them, and there are many similar cases of philosophies surviving and exercising the influence they do because they are subsidized by institutions of various sorts. And sometimes this is at least as influential as anything to do with the ideas or philosophers themselves.