Frequency Filtration
To expand on Brian, making a filter with analog components that has a very small passband with a fast transition into the stop band is nearly impossible, while this is very very easy with a digital system.

You will have to sample at-least twice as fast as the fastest signal. I would suggest making sure you are at-least 2.1 times faster.

For will need to design one gigantic filter that changes each frequency by the amount you want. 

If you want to control the magnitude of each signal separately then you will have to make N digital filters, create N datasets, apply the N different gains, and then recombine the signals, if you filtering is good you will just be able to sum to recombine. Do not take too much solace in this as it is the only easy step.

The sharper you want your transitions the more data-points the filter will need. There is no way around this, it has been proven mathematically. 

Let me know in a comment if I can add more to help.