Unfortunately there is no way to obtain 16 input channels at 44.1kHz with the multiplexer capelet. The ADC part in use is capable of performing 500000 conversions per second (500ksps), which limits the theoretical sampling rate at 16 channels to 500000/16 = 31.250kHz. However, this is still an optimistic figure because it does not take into account the time that would be needed to communicate with the ADC. I would expect the realistic upper limit to be somewhere around 15 to 20kHz. Achieving that, however, would require a rewrite of large parts of the PRU code. The PRU is the on-board microcontroller that performs the I/O operations between the CPU and the ADC and DAC. One possible solution to achieve larger sampling rates (which would still require rewriting the PRU code) would be to add another ADC chip of the same type, thus achieving 1 million conversions per second. You could either build a dedicate breakout for it, or buy another Bela cape and jumper it to your existing setup. Be aware that this is a complex undertaking, and will require a significant amount of time, especially if you are not familiar with the PRU.
Also, in case this is relevant for your application, keep in mind that sampling of the 16 channels is not going to be synchronous. Each analog input channel would be sampled a few microseconds apart from each other.