I'm not sure precisely what you are referring to, but my best guess is that you ask for a harmonica that has two notes, one octave apart, with a tone that beats like a tremolo harmonica.
In a normal tremolo, there are only two notes that interact, and only one parameter to consider, namely the difference in frequency. Varying the difference changes how fast the perceived tone is beating, very simple. If we now instead have two reeds tuned exactly one octave apart, and two reeds which are identical to the first two but slightly sharp, things get more complicated: how do the two beating tones interact? Will they beat in unison, or will the beat frequencies be slightly off? If so, the beat frequencies in turn will create a beat together! This could make for some strange sounds.
I have no idea how this would sound on a real harmonica, but I did some plotting.
Say that we have four reeds, two tuned exactly one octave apart and two identical to the first but slightly sharp. Say also, to simplify things, that each read produces a clear tone without overtones. If we sharpen them by the same amount, equally many cents exactly, we get the following waveform, zoomed out to see the beating, we get the following:
If we instead raise the higher note by just half as many cents as we did the lower note, we instead get this:
Much more similar to the normal interference of the tremolo.
But (there's always a but!) if we raise the upper note by 55% instead of 50% of the amount that we raised the lower note, this happens:
The precise intervals really matter! This shows a pattern that is changing over time, a sort of tremolo of the tremolo
A real harmonica is of course not as simple, but has a number of overtones, acoustic interactions between the reeds and so on, so these highly idealized examples might not fully reflect what really would happen. They give us a hint, however, that things might become quite a bit more complicated when we introduce more reeds
Edit: Just to be clear, the pictures are simplified, in that they show interactions between completely pure tones, without overtones: pure sine waves.
Edit2: Fixing some typos and clarifying a few statements.