To me, it looks like the lights are arranged in three strings or chains, to allow different colours or flashing patterns & sequences?
One common positive power connection (VCC) and three separate returns that each have the negative switched to control them; LD1, 2, 3.
The CDS1 terminals look to be for a light dependant resistor, the photosensor.
The big problem with trying to connect anything else, is that any lights you connect must be able to run from the battery voltage and not take too much current.
Light strips are readily available that use similar connections - but the commoner types operate on 12V and need a lot of current.
There are a few types made for battery powered devices however.
Examples - these types of strips could probably be wired to your controller:
**broken link removed**
FeaturesChanges Colours,RGB,Waterproof. LED RGB Light Strip multi-color. 1x LED RGB Strip 5V. 1x LED RGB Strip 5Vwithout remote. If the battery power is low, it might influence the normal function of the strip light.
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If you look at any others, be sure it says they work from a three cell battery box.
I'd guess you may be able to make your own, but each LED in each string would need an appropriate resistor to allow it to work from between 3 - 4.5V over the life of the batteries, and the total current for all LEDs in each string no more that probably 100 - 200mA, depending on how often you are willing to change the batteries.
If the current is too high it may damage the tiny transistors that control the outputs, as well as draining batteries quickly.