Bode plot horizontal asymptote

[Teszla]

In a bode plot for a low pass (or high pass) filter, what is it that determines where the horizontal asymptote will be?

If we have for example a LPF with only a resistor and a capacitor and take the voltage over the C as the output signal, the horizontal asymptote will be at 0 db, since for low frequencies the signal is unfiltered. But if we want the horizontal asymptote to be at another value (i.e. all frequencies to be filtered with -X db), how is this found?

 

[LvW]

.....all frequencies to be filtered with -X db)

All frequencies ?

Or do you want a filter with gain like an active filter?
When the horizontal asymptote is required to be below 0 dB use another resistor in parallel to the grounded C.