How many times can you split a line level signal with a Y cable before signal degradation?

[olds1959special]

No idea. I'd have to measure the resistance.

I can try to measure with a multimeter.

 

[Speedskater]

The resistance of the splitter better be a small fraction of a single Ohm.
(it will take a rather good meter to measure that low)
However the input resistance of each component should be at least several thousand Ohms.
* * * * * * * * * * * *
There is one concern:
Some older components, short their input with a diode when switched off.
So in this mode of operation, it will cause distortion in the other components.