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There are more than three amplifiers in a typical radio receiver.

If, however, you are asking why there are three "stages" in the IF section, then the reason is that the IF section of a typical superhetrodyne receiver needs more bandwidth than can normally be provided by a single stage. As a result, there are usually three stages, each tuned slightly apart, so that you get a reasonable bandpass - otherwise, the demodulated signal will suffer.

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