We present a low-temperature ͑mK͒ magnetotransport study, using intense pulsed magnetic fields to 50 T, of two double GaAs quantum well, triple AlAs barrier resonant tunneling structures, which demonstrates the critical influence of the second quantum well on the tunneling behavior. We show that charge accumulation in the first well, and thus the overall tunneling characteristic, is controlled by the position of the lowest bound state in the second well, and identify tunneling transitions that are unique to triple-barrier structures. We also demonstrate that the tunneling current is sensitive to integer and fractional quantum Hall effect states, and find that the voltage-tunable accumulation of charge in one of the samples provides an unusual environment for the study of ground states of a two-dimensional electron system. ͓S0163-1829͑96͒06431-4͔