Does increasing the amplitude of a signal also increase the data rate?
Increasing the signal increases signal to noise ratio therefore the data rate can rise: -




C is the channel capacity in bits per second;
B is the bandwidth of the channel in hertz (passband bandwidth in case of a modulated signal);
S is the average received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watts (or volts squared);
N is the average noise or interference power over the bandwidth, measured in watts (or volts squared); and
S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels). 


The bandwidth remains unchanged although the extreme edges of the bandwidth may now spill over into closely localized channels due to overall higher power. In other words, in a practical world, tighter bandwidth filtering may be required. I'm thinking radio as a good example. But generally more signal means more bits per second.