every 1->2 splitter has a damping of 4 - 6 dB (depending on quality).
When you have 3 splitter you have signal loss 12 - 18 dB . That's a lot.
You better replace the old stuff. Nowadays there is a lot interference of 4G. Old cable and old splitters are not good anymore.
The situation I have. 1 main lead into a line amplifier (max 25dB). After the line amplifier I have a 12 output divider (most people have 4 or 6 output). The first output lead has a damping of -12.5 dB , the last one -24 dB.
I tuned my amplifier so that the signal output of the last (-24dB) has the same level as the main lead.
The outputs with less damping (-12.5, -13.5, -14.5 .....) I use for the longest cables in my house (to bedrooms) and the outputs with the highest damping (.....-23, -24) I use for the shortest cables. This way I have (almost) in every room the same signal level as the main lead.