Mario Bunge (R.I.P. 2020) proposed strong philosophical assumptions underlying the process of making science. I would recommend La ciencia, su método y su filosofía, 1960, Mario Bunge (don't know of english translations). Probably there's a lot of more from him in english, he was quite prolific, a great philosopher of science and an amazing epistemologist, and I'm far from reading 2% of his work. Following, what I remember from reading him, which could answer your question.
This is, in simple words, what the scientific method is about (at least, an interpretation of Bunge's ideas, I tried to be as precise as possible).
First, knowledge is more or less a model of reality that is built in order to increase the probabilities of survival. Second, knowledge is subjective. Third, scientific knowledge is just some type of knowledge, which is build using the scientific method.
"Using the scientific method" could be subject to multiple debatable interpretations. One of my best teachers (using the aforementioned book) stated that the scientific method just reduces to reach the optimal level of objectivity (which has the goal to allow the communication of knowledge, in order to be useful for others, in order to survive). What does it mean?
Considering the previous three statements, the fact that knowledge is subjective means this: you know the sky, I know the sky, but the concept sky is not objective: it is the result of multiple experiences of each one of us; then, it is subjective for each one. But take into account that such experiences are necessarily different (otherwise, it would imply that you and me are the same individual). Therefore, at least, our knowledge of the sky is a shared subjectivity. If we talk about it, we can assume that we agree on multiple facts about the sky, but by doing that, we will not reach objectivity. That's just sharing inter-subjective knowledge (my phrasing, not Bunge's). Religious knowledge is usually inter-subjective.
When would we state that some knowledge is objective? When can we trust that communicating knowledge is safe? The answer is this: the moment you and me apply a method that both agree on, and that make knowledge as objective as possible, so to be communicated, and used for survival.
That's precisely the scientific method. A convention, an agreement on how to reach an optimal level of objectivity. An excess of objectivity would be undesirable (we don't need to describe in excessive objective detail where are the atomic limits of solids in order to agree that adding 1+1 solids results in 2 solids). A lack of objectivity is undesirable as well (I could affirm that God exists because I had a dream, and you should agree). The scientific method produces a category of knowledge that we agree on by convention, which can safely be communicated to others that need it. As you see, there's a lot of issues to agree on. That's the philosophy of science, which could be a huge amount of propositions and rules.
The philosophy of science must not be misunderstood with the knowledge that is product of science. The philosophy of science is our agreement on how to develop knowledge that aims towards our survival. The scientific knowledge is such knowledge in itself.
See for example the historic development of the thermodynamic laws. The first three laws were created and nobody noticed that there was a huge subjectivity embedded on them: the concept of temperature. Temperature is a feeling, not a physical concept. But that was quickly solved, just by adding a previous law (the zeroth-law), which defines in objective terms what is temperature.
That is the process of the scientific method. Not necessarily what common literature describes (observations, hypothesis, testing... etc.). So, it is clear that the scientific method does not reduce to a short and rigid set of rules, but rules are useful in multiple contexts.
Bunge makes a deep analysis not only of the complexities of such process but also of the problems of communication, the epistemic issues (how to deal with multiple types of knowledge?), the pragmatic consequences (a discipline would be characterized from three dimensions: science, technique, art), etc. Highly recommended.