We have developed a multi-channel, multi-frequency EIT system with operating frequency of 10Hz to 500KHz. The number of digital voltmeters using phase-sensitive demodulation can be varied from 8 to 64 and we found that 16 and 32-channels are most practical. This paper describes the design, implementation, and construction of 16 and 32-channel systems. The performance of the system was thoroughly tested and we found that CMRR of the developed voltmeter is about 85dB with $100{Omega}$ unbalancing series resistor. The SNR is greater than 99.6dB and the output impedance of the constant current source is $1{Omega}W$ at least for all frequencies. Imaging experiments using a banana with frequency-dependent conductivity and permittivity show that frequency-difference imaging is possible using the developed system. Future works of animal and human experiments are discussed.