Nonlethal Force said:
Yes, but the OP wanted to make both attacks with the light side, not make the light side more than the one-handed side. As far as I know, there is no non-magical way to make two attacks with the off-hand side of a double weapon without Improved (or Greater) TWF or intentionally using itterative attacks with the off hand.
As per the SRD:
Two-Weapon Fighting
If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon.
and
Double Weapons
You can use a double weapon to make an extra attack with the off-hand end of the weapon as if you were fighting with two weapons. The penalties apply as if the off-hand end of the weapon were a light weapon.
So if you use Two-Weapon Fighting with the quarterstaff, only your added attack is with the off-hand side. Say both ends (A and B) have different properties. You have a +6/+1 BAB.
Regular attack: +6 with end A or B
Full attack: +6/+1 with end A or B, but both attacks must be with the same end.
Double-Weapon Full Attack (with TWF feat): +4 with end A (one-handed), +4 with End B (light weapon), -1 with end A (one-handed).
EDIT: Following from this, let's take our fighter from the previous example. BAB of +6/+1, STR of 10, DEX of 18, Weapon Finesse, and Two-Weapon Fighting. Quarterstaff end A is cold iron, B is silver.
Regular Attack: +6 with end A or B. A quarterstaff is not finesseable in this use.
Full attack: +6/+1 with end A or B. Also, not finessable in this use.
Double Weapon Full Attack: +8 with End B, +4 with End A, -1 with End A. This is because the off-hand attack (End B) is the only light weapon being used, and thus the only one that benefits from Weapon Finesse.
Until you hit Improved Two-Weapon Fighting, you cannot get more than one attack with the finesseable end, no matter what you do
UNLESS the off-hand end has the Speed enchant, which would allow it an extra attack at your highest BAB. In which case if End B has the Speed property, our fighter would attack at: +8 with end B, +8 with end B, +4 with end A, -1 with end A.
Which leads to another question - if you're using Two-Weapon fighting and BOTH weapons have the Speed enchant, you get
two extra attacks, one with each? Dang, that could get abusive. No wonder it's so expensive.