You should not need the second amp unless something is wrong.I use one pre-amp with three antennas( one is a home brew) going into a good switch, then into the pre-amp. Using the pre-amp I've found that usually one of the antennas will bring in less noise, depending on which band I'm listening to. I'd rather lose the pre-amp than one antenna; antennas are more important, in my opinion.
Yes N_Jay, I'd like to second that.Multiple amplifiers are (almost) never any benefit in a receiver system.
The sensitivity is set by the first amplifier (mostly by the noise figure, not the gain) and all the second amplifier does is add noise, intermodulation and potentially overload the receiver.