1H NMR of p-methoxy phenol, 32 possible lines?
I think your theory is correct, but my tests were inconclusive. You can try your own hand at simulating the spectrum, for instance with Hans Reich's program DNMR. It resulted in the following:



This is the downfield half of the spectrum. I did not attempt to replicate the experimental spectrum exactly, it's only to illustrate. I used the following parameters: 


$\sigma_A = \pu{7.5 ppm}$
$\sigma_X = \pu{8.19 ppm}$
$J_{ortho} = \pu{8 Hz}$
$J_{meta} = \pu{3 Hz}$
$J_{para} = \pu{0.5 Hz}$


On to your question. If you increase the J sufficiently, while retaining symmetry among the J, you get...

 

... 20 peaks! (only one set of multiplets is shown, so the total number of peajs is twice the number visible above) . I continued tinkering with the values, and breaking the symmetry among the couplings led to ...



... 26 peaks!

Presumably breaking the symmetry in the shifts will increase the number of peaks further, but surprisingly this had just the opposite effect.

But this is not the most illuminating approach. Better would be better to dig into the QM.