In attorney-authors Pressman & Tuytschaevers' book Patent It Yourself, in the section on responding to rejections based on combinations of multiple prior art refs to achieve the same result (18th edition, pg. 397, item #41), it is stated that dependence on a combination of more than 3 refs can be argued to be evidence of nonobviousness. In practice of countering this type of rejection, how successful has this form of argument been?
It is unfortunately common for US examiners to combine 3 or more documents to argue obviousness. I recall once having 6 documents cited in combination (which, predictably, we did not react kindly to). While there is generally some need for the examiner to articulate why the combination is made, there is a wide range of ways they can do so. MPEP § 2143 provides quite some discourse about this. Notably, while an explicit motivation to combine in the prior art is one rationale, it is only one of many.
Because of this, in my experience, examiners generally do not yield to arguing simply that there are too many documents. That is, while such an argument has merit on a theoretical level (since the skilled person has to combine lots of different teachings from different areas, then it seems less obvious), in practice I can't see that winning you the case. You would typically need to show either something undisclosed by any document, some incompatibility between the teachings, or some kind of teaching away.
As a comparative note, at the EPO it is very rare for an examiner to combine 3 or more documents (though 2 is common). This is because EPO examiners take the requirement for the skilled person to have a good reason to add in each document a lot more strictly. There, multiple documents are a strong secondary indicator of an inventive step. Indeed, it is entirely possible to successfully argue that the skilled person would have no reason to combine even two documents, in the absence of some suggestion in the art to do so.