the excerpt in the picture is four-part drop 2.
I do not know what to make of the beamed notes under Cmaj7?
The first stack of notes seems to suggest Cmaj7 alright, but 2nd and 3rd stack of notes seem to suggest Dm7 and Em7, but no chord labels are applied.
Do I see them as implied chords(wholly different passing chords), or do I see them in relation to Cmaj7(i.e C is 1, F is 4, and so on...)?
Beat 1 is Cmaj7 and at the syncopated onset of beat 3 there is an E7 chord, but the extension given of (♭13) probably makes clearer sense as an augmented chord, like Eaug7, because the base triad is augmented and the only extension is the seventh.
The stuff in between those two chords is passing motion, unless there is something compelling to make it identify some other way. On-beat accent could be one such compelling reason, but in this case that "chord" would be some type of either iii chord, which is often regarded as having a type of tonic function, or substitute for a tonic chord, or all the pitches make sensible pitches for the continuation of the beat 1 C chord with the additional of the D extending it to Cmaj9. In other words we have passing motion only on the up beat of 1 connecting an "arpeggiation" of a Cmaj9 chord, which then moves to the Eaug7 chord.
Regarding comments on your post: your wording of "treat" versus "what to make of/see" was a bit confusing. "Treat" seems like a question of "how to execute" while "what to make of" seems like a question of "how to analyze." Not a big deal in casual conversation, but maybe unclear in writing. In this case the rootless voicing of Cmaj7(9) on beat 2.
Also, FWIW, the chord symbols in the example, can act like a sort of analysis, but they are really queues for rhythm section players, like bass, piano, or guitar. That has bearing on the analysis side of things, because it assumes that the rhythm section will in some fashion: (1) contribute the appropriate bass pitches, which in this case will be the chord roots, and (2) possibly comp the chords through the duration of the passing motion. That can mitigate certain ambiguities with partially voiced chords in the notated parts.
The reason there are no chord symbols under the second and third eighth notes is because the underlying harmony on the first two beats is Cmaj7 until the E7 on 2+. One of the possible ways of harmonizing stepwise eighth notes over a static chord is to harmonize the notes on the beat as tonic chords and the notes on the up beats as diatonic passing chords. This is what is done here. The Em7 on beat 2 is really a Cmaj9 with no root in the horn voicing. In this case the 9 is the melody note. Excluding the root or substituting it for a 9 is very common when writing for horns. You can see that the A7 chord also has a 9 replacing the root. The bass will cover the root and the 9 gives you a more colorful sound.
Chord symbols don't always tell the whole story. In this case, the symbols describe the basic harmony, the notation adds detail and complexity. You are correct that Dm7, Em7 could have been added as additional chord symbols.
If chord symbols could fully describe a piece of music, we wouldn't need notation!
