The more ICs I add, the less stable my circuit is. Why is that?
Add a 100nF capacitor across power supply pins of every single IC and a big 47uF or 100uF capacitor once on the power rails of the breadboard. Keep the connections between IC and 100nF cap as short as possible.

The 100nF decoupling caps are much better than electrolytics (like your 47uF) at suppressing fast transients caused by the logic inside the IC's switching.