The Chomsky & Halle 1968 theory is not very clear, in that they predominantly talk of a single matrix containing all features, but there are some anomalous statements that suggest thinking about having two parallel matrices. One of those statements is p. 297 that "the phonetic representation can be thought of formally as a two-dimensional matrix in which the columns stand for consecutive units and the rows stand for individual phonetic features". In light of the fact that diacritics, rules-exceptions and morphosyntactic properties are also features, this segregation of phonetic features at least at the phonetic level suggests that somehow nonphonetic features eventually fall out of the picture, encouraging one to think that they are separate. Same page, they also say "In the case of the phonological matrices...", which would only make sense if there are nonphonological matrices that the phonological matrices are distinguished from.
One thing that does not reveal anything about their ideas about matrices is the use of square brackets. As they said above, the phonetic representation is "a two-dimensional matrix in which the columns stand for consecutive units and the rows stand for individual phonetic features". They do not say that the phonetic representation is a vector containing segments and that a segment is a vector containing features. Thus "matrix" in their view is not the same as segment (or boundary). However: in rule-writing, it is standard that [a,b,c] represents a single segment and [a,b,c][d,e,f] is a sequence of two segments, that is, the graphic object square brackets does represent a segment. In light of that, it is impossible to infer anything about the "matrix" status of nonphonological features by inspecting the form of a rule referring to the two kinds of features such as p. 355 (71) [-αsyl,αcons] → φ / __ # [-αsyl,+foreign]: the brackets simply mean "that segment".
Section 7 of ch. 8 addresses nonphonetic features. On p. 374 they postulate a convention that "all nonphonological features of a given lexical item are distributed to every unit of this item" ("item" = morpheme, "unit" = boundary, segment). Then continuing, "if a given lexical item is a human noun in the kth declensional class which is an exception to rule n, then the feature specifications [+noun], [+human], [+kth declensional class], [-rule n], now reinterpreted as on a par with phonological features, are assigned to each unit in this lexical item. The problem is understanding the expression "now reinterpreted", which suggests a derivational change, for example "two matrices merge into one" (but unmerge so that nonphonological features aren't present in phonetic representations??). This (merging) is what I think underlies Leben's theory.
The bottom line for SPE is that they are not explicit about the 1 vs 2 matrix question, so we really have no idea what they were thinking (nor do we particularly care about their private thoughts).
Leben in his dissertation (sect 1.0.2) embraces the idea of multiple matrices:
Most phonological features appear to be capable of only one type of
representation; for example, features like [continuant] or [strident]
are almost universally maintained to be features only on segments,
while features like [+Past] or [+First Conjugation] are represented as
features on morphemes or larger units.
His notion of representing grammatical features "on" morphemes resolves the mystery in SPE as to which segment(s) underlyingly bear a diacritic feature – that is, if -akwo- is [+past], which segments underlyingly bear that specification? Although there is a convention that would distribute such a feature to all segments in the morpheme, nothing prevents underlying forms from having nonphonetic features contrastively located on segments within a morpheme. Leben's theory, with matrices "on" different things, resolves this matter: each morpheme has a single matrix of nonphonetic features (also tone).
So, Leben's theory is the second kind of matrix that you ask about. SPE may have thought of having such a thing, but Leben embraced it, and planted the seeds of autosegmental phonology in that soil. Nothing in principle would preclude creating a number of different kinds of matrices and associated units, for example "word" or "syllable", and since morphemic phonetic features (tone) can migrate into the segmental matrix (via what he calls "tone mapping"), and since this can be language specific, then the floodgates are opened somewhat.
I should add that understanding the history of these concepts is extremely difficult (was agonizing at the time) because of the unclarity of the original authors. This gave rise to many different interpretations, where I think Leben saw his analysis as being consistent with the SPE account and he only added a little change. The status of "matrices" and "segments" in SPE phonology is quite unclear, and became "clear" only subsequently, often made clear by critics. What is clearly understood is that in SPE phonology, there exists a "unit" (segment or boundary), and the phonetic features contained in that unit have no further structure -- there are as many instances of a feature as there are units. The term "matrix" is typically used to refer to "a unit", but the original canon (SPE) is quite murky. The appendix on formalism defines the objects for writing rules, but there is no corresponding formal definition of the objects that rules act on. The gesture in the direction of 2 special symbols (→, φ) and 3 classes of things (features, specifications, categories) as the primitives of rule theory, and it is completely unclear how parsing elements (brackets) fit into their theory.
