There have been synoptic theories proposed with more than 2 sources, and theories with a mix of oral & written sources, but they have tended to be less popular than the Two-Source Hypothesis, Farrer Hypothesis, and Two-Gospel Hypothesis.
- Robert Lindsey's theory proposed 3 hypothetical written sources (further
- Rainer Riesner proposed 6 hypothetical written sources + a variety of
oral sources (see The Synoptic Problem - Four Views p. 107)
- Eichhorn suggested 6 hypothetical documents (see William Farmer The Synoptic Problem p. 10)
- Heinrich Ewald proposed a 9-document hypothesis (ibid p. 25)
These and other "complex" theories have been criticized on at least two grounds:
- The contents of a hypothetical document are speculative -- the interactions between hypothetical documents grow exponentially as we increase the number of documents, significantly increasing the opportunity for error
- They fail the Occam's razor test (don't multiply entities beyond necessity); thus, they are generally only appealed to if there is no possibility to explain the synoptic data on a simpler basis. As William Farmer summarized:
This does not mean that the investigator should assume that there were
no additional hypothetical documents. On, the contrary, he should be
open to the possibility that such actually existed. There are
instances in literary-historical studies where circumstantial evidence
requires the investigator to posit the existence of a document for
which he has no direct evidence. But a critic should not posit the
existence of hypothetical documents until he has made an attempt to
solve the problem without appeal to hypothetical documents. Only after
the investigator has been unable to understand the relationship
between Matthew, Mark, and Luke without appealing to unknown sources
is he justified in hypothecating the existence of such sources, in
order to explain phenomena otherwise inexplicable. (ibid p. 209)
Farmer himself (and many others) found it possible to explain the phenomena of the Synoptic Gospels without the need to appeal to discrete hypothetical documents. This doesn't mean the synoptic authors did not have other sources (oral and/or written); it means we don't have enough data to reconstruct them.
Luke's independence from Matthew is one of the two critical pillars of the Two-Source Hypothesis (the other pillar being Markan Priority). If Luke used Matthew as a source, there is no need to appeal to Q to explain the more than 200 verses shared by Matthew & Luke that aren't in Mark.
Both the Farrer & Two-Gospel Hypotheses accept that Luke was familiar with Matthew's Gospel and, as a result, claim that it is possible to explain all of the relevant synoptic phenomena without the existence of a document like Q.
One of the difficulties with hypothesizing Q as a single text (or hypothesizing any other discrete source) is that whichever of the synoptic authors wrote 3rd does not treat his sources consistently. If, for sake of argument, we accept the Two-Source Hypothesis, we find Luke's handling of Q material wildly inconsistent with his handling of Markan material (this phenomena is admittedly technical--there's a deep dive on this on my channel).
Early Christian historians held that all of the canonical gospels were based (at least in part) on the testimony of ear/eyewitnesses--Luke claims to have relied upon several of them (see Luke 1:2) Their memories cannot be reconstructed as a discrete source the same way a document can.
If the Synoptic Gospels were all written within a generation of Easter (see the works of John Wenham or Bernard Orchard, for example), the need for a "complex" solution to the synoptic problem diminishes, because the stories still existed in human memory. Sources like "M" & "L" would not necessarily have to be written documents at all.
Hypothetical documents stir curiosity because, like the human imagination, they can go anywhere, do anything, or say anything.
Virtually all synoptic scholars acknowledge there were teachings & stories about Jesus in both oral & written form besides the canonical Gospels. However, most acknowledge that our ability to reconstruct those lost sources is limited. Scholars who wish to minimize speculation tend to focus principally on sources that can be directly examined.