Where should an increase in harmonic frequencies go in the Nyquist formula?
Yes, your capacity increases. If your bandwidth is limited to 8Hz you can just have one sine period per 125ms, and that sine can represent 3 bits of data if you modulate 8 levels in it. That could be 8 levels of amplitude, but also a combination of for instance 4 amplitude levels times 2 phase levels. So 8 periods per second \$\times\$ 3 bits \$\times\$ 2 = 48bps like you said. (I'm not sure where the factor of 2 comes from, but I'll assume it is correct.)
Adding up to the fifth harmonic will get you 5 sine waves in the same 125ms, each of them able to represent 3 bits of data. So that gives you 5 \$\times\$ 48bps = 240bps.  

If you would use the larger bandwidth to construct an approximation of a square wave, you're not using the extra information capacity of the higher harmonics. That's because phase and amplitude of those harmonics would be determined by the phase and amplitude of the fundamental to create the square wave, and they wouldn't carry any information of their own.