Well, the immediately obvious thing is that you can work with less layers, constantly merging as you need. That will get you to an end state, but at the cost of making it harder to undo and redo sections of your work. That's okay, if you want to emulate working in traditional media, but that's giving up a lot on the power of digital.
So, how do you do it digitally? Copy canvas is going to be your friend. For the sake of illustration, I'm just going to use a 500 x 500px document on my iPad pro and pretend that it can only support about 5 layers.
Step 1: Create your document and start drawing
As you can see, I've hit the layer "limit" and the cartoon is incomplete!
Step 2: Copy Canvas (swipe to the left and select duplicate)
I named it stage 2 to indicate that it's the second stage of my drawing.
Step 3: Edit next stage
First, flatten the canvas by pinching existing layers together, then create your new layer and continue editing.
Oh no, layer limit again and still not done!
Step 4: Copy Stage 2 Canvas
Step 5: Edit Stage 3
As before, flatten the canvas and continue editing.
This time I finished with layers left.
So, you might be wondering, what happens if I need to change something in, say, stage 1? Like, for instance, I want to change his eyes. In that event, you can make your changes, open the "wrench" icon at the top and copy the canvas, open the next stage, delete layer 1 and paste. Move the pasted canvas to the bottom. Perform the same steps in the second stage, and paste into the third stage. Keep going based on the number of stages, you need to propagate along as needed.
Like I said, this is a bit of a fussy process, but if you're being severely limited in the number of layers you can get because of your iPad, this may get you further along and still preserve your layer work.
A limitation to note... If you do need to copy canvas to propagate a change from an earlier stage, it will take the background along, so the bottom layer will lose transparency.