As an option to the pre-amplifier you could use the 8 way distribution amplifier as recommended by @teleview. If the 4 way and 3 way are in different locations you could use a two way drop splitter (available at
www.solidsignals.com) before the location of the 4 way. The output with the higher loss should hook up to a CM3014 4 way, distribution amplifier (this replaces your 4 way splitter) and the low loss output should run downstream to the 3 way splitter. That would more even distribution of your signal and prevent overload at any location.