A veteran accordion technician once told be that melodicas were really intended to play one note at a time.
That being said, you will see people playing polyphonic music. I like to play chords and intervals in accompaniment to music as well. Mostly I chop chords loud and quickly, or play them softly so I can sustain them for a long time.
The bottom line is, playing the lowest bass notes while trying to play high lead notes on a melodica is not the melodica’s forte.