Some time ago, someone asked if they could increase the range of a vco
by adding another varacap diode in parallel with the existing one. The
answer given was that it wouldn't change the tuning range, since the
min-max capacitance ratio didn't change. The answer sounded technically
correct, but also counter to gut feel. As it turns out, it is only
partly correct.

Consider using conventional tuning capacitors. Hammarlund used to make
a line of double bearing variable caps in a range of max capacitance
ratings. The principle difference between the family members were the
number of plates. The 25pf variable would have had about the same
min-max capacitance ratio as the 50pf variable. Yet ham lore had it
that the 14Opf (well 140mmf in those days) would give a 2:1 frequency
tuning range, and a 350pf unit a 3:1 frequency tuning range. In
practice this did work out.

The reason is that it is the TOTAL capacitance across the inductor that
resonates it to a given frequency. This includes the distributed
capacitance in the coil, any stray wiring capacitance, and capacitance
found in any parts (such as tube grid to cathode or fet gate to source)
connected to the tuned circuit. If the inductor is fixed in value a 4:1
capacitance ratio is needed to give a 2:1 frequency range in a tuned
circuit, 9:1 for a 3:1 frequency range (ie: capacitance ratio is the
square of the frequency ratio).

Now consider a varicap tuned circuit using diodes with a 5:1 capacitance
ratio (say 10-50pf). Our inductor has 5pf of distributed capacitance,
and there is 10pf of stray wiring and other capacitance. We would thus
have a 25-65pf tuning range or a ratio of 2.6:1 (not the diodes 5:1!)

If we were to add another varicap in parallel the diode tuning range
would be 20-100pf, still 5:1. We now need a smaller inductor, so our
distributed capacitance drops to maybe 3pf. The stray capacitance
remains at 10pf. Now our tuning range is 33-133pf, a ratio of 4:1.
Our original tuning ratio was 1.6:1, with the extra diode it would be 2:1.

So the original answer that adding another diode wouldn't double the
tuning range is correct, but it would make some improvement.