Is the OP question about playing "two parts" focused on, one part being melody, and the other the bass accompaniment? I think that's the question, and I see the other responses here are taking that as the question, but I'm hair-splitting bc I'm not 100% sure what the OP is asking.
But if that IS what you are asking, Anglo is not the optimal concertina system for that type of playing. You CAN do some amazing stuff on Anglo in this vein, with creative arranging, and there are regulars on this very site who do that kind of magic. But the number of keys you can do it in, is limited. On a 30-button, you do not have all notes on the left-hand bass side, and you don't have all notes in both directions on either side. On a 38/40 button, there are ergonomic issues that interfere with having full free rein for this kind of arranging.
In Irish trad, the Anglo players don't care about these limitations, because ITM is largely melody music. There are bass effects, but it's constrained. There is a contemporary trend of playing more bass chords than they used to, but they do it in the keys that work for that on their Anglo, and don't do it, or just do a double stop or such, for the rest.
RE English system. It is ironic that the so-called "treble" system is known as the typical session EC, because as the OP points out, it wastes much of the layout with ridiculous high notes no one uses, and wastes the ergonomically most comfortable part of the concertina end where your fingers fall naturally, on those very ridiculous and useless high notes.
The stupidity is further compounded by the fact that the Tenor EC, like the treble a 48-button layout, but minus the super-high notes and plus some really useful lower notes, is stereotyped as being for backup to singers and super-hard to find unless you have one built new. In fact it may be the most brilliant concertina for dance-derived instrumental world folk music, particularly if you need to play fast, and like a melody=prominent sound. You can play melody or chords in any key in either direction, and the whole range is comfortable to your hands.
The caveat being, if you want a literal rhythmic bass constantly under your melody, like, bass-chord-chord waltz oompah . . . it "can" be done on an EC. But it's pretty tough. Not too bad for the hands. For the brain. Because of the bilateral layout. Your chords will be split between sides, and your melody notes are switching sides as well. But you can get great effects by doing that for a couple of measures here and there at the same time as your melody note, plus, doing it in the "spaces" where the melody pauses. Where "pickup" or filler phrases go that connect the A and B parts, etc. It gives the impression to the listener, that a bass line is going the whole time, when it really is not. A wonderful example of Tenor EC arranging on instrumental folk is the CD "Black Boxes," by the UK musician Sarah Graves, who plays two ebony-ended Tenor 48s on the recording, an Edeophone Tenor 48, and a Wheatstone Aeola Tenor 48.
However, if you want literal, perpetual rhythmic bass under your melody for the complete, entire duration of the piece, the fact is, that is optimally done on a duet. Is there some reason you don't want to go duet?
Edited by ceemonster, 18 February 2018 - 04:23 PM.