Not sure how I missed this thread, but let me add a couple of ideas.
As Melodica-Me suggested, reverb and delay are the bread and butter effects that bring a professional sound to the melodica. I almost always play with one or the other. EQ is nearly a must too to shape your sound, though it is less important when playing with HM-26/27/32s as you can shape the tone through playing techniques.
I have tried adding many multi-effects to my sound using multi-effects processors. They are fun and some serve the melodica well, but lately I am trying to get a natural sound, keeping things simple for live performance, and learning to get the sound I want through technique.
It is easy to have unrealistic expectations about amplified volume with a microphone. Sound reinforcement at it best is just that, sound reinforcement, not huge amplification increases. If you are in an arena, you need a great soundman. If you are playing the local winery or restaurant, you want to reinforce the natural sound of the instrument without changing its character. You may be expecting too much from an amp. I do want my effects to come through the amp, but now I accept a blend of the natural sound and the reinforced sound.
I find the melodica is a loud instrument relatively speaking, I can drown out my acoustic guitarist easily. Actually, I sometimes have a hard time playing soft enough while still being able to get the melodica to sound right.
I fought with this amplification issue for a long time. Now I am able to relax and in most playing situations, get the reinforcement I need while still letting the instrument speak on its own.
Finally, I am getting pretty good volume from both a stage monitor and a guitar tube amp. Usually I can get the volume controls of these amps half way up and get good volume when needed. I use an SM57, a pedal or two, and go straight into the amps. Mic and amp placement are key, as are effect settings. I find if you are using multi-effects or many pedals, feedback control becomes much harder. Tell us what you are doing specifically, and maybe we can offer specific suggestions. I would start with the mic straight into the amp and see what volume you can get. You might be surprised. Then add effect pedals one at a time and see how each one reduces your ability to achieve the same volume as going straight into the amp.