The Crestron will do it if you go high enough up the price and ability ladder to get the units that accept multiple antennas.

I have solved this problem more simply with house-wide control of four Sony satellite receivers.

You will not find a system with a strong RF signal, so you have to make a system with a sensitive and wide area coverage antenna.

We placed three antennas around the house and were able to run the antenna signal DIRECTLY through CAT5 (all that was available in the walls), literally splice them together, use an adaptor to go to an F connector into a 20 dB wideband amp (54 mHZ - 10000 mHz), then split the signal four ways to go to the four satellite receivers.

RG-6 would have been better, but there was none available in the walls. The wideband amp was necessary because the remote was on some VHF or UHF frequency, but we did not know which, so we covered our bets. If it was between OTA 13 and 14, a VHF/UHF amp would not have amplified it because they do not cover all frequencies.