Yes, it may yield 3+ actions per attack.
With your Knock-Down feat, anytime you deal 10 points of damage to a target in a melee attack, you get to make a free trip attack against that target. With the Improved Trip feat, you get to immediately make a free melee attack against that opponent you just tripped.
Without the Knockdown feat, in order to trip, you make a touch attack against the target, then perform your trip roll. Some DM's may rule that you cause no damage with that touch attack (as I do; however, I do allow falling damage since they do hit the ground against their will).
During an attack of opportunity, that is not on your turn, by it's feat description, you should be allowed to perform a free trip attack if you successfully deal 10 points of damage on your attack of opportunity - possibly nullifying your opponents action. As a DM, I would allow this, simply because there are other feats that have that same philosophy, such as Close-Quarters Fighting (it can interrupt a grapple made towards you). Once again, you should be allowed to get your free melee attack against that successfully tripped opponent; some DM's may rule that is doing too much or going to far.
Speak with your DM to iron out all the details before you start piling on the feats for a trip build. Hell hath no fury like a DM scorned. Pulling zingers on your DM will ruin the fun for the rest of your party, and will get DMG's thrown at you.
With iterative attacks, assuming you have BAB +15, your three melee attacks have the potential to provide you with a free trip attack, and the free melee attack with a successful trip.
These iterative attacks must be done with a trip weapon, or with unarmed strikes. Since there is nothing in Improved Trip's description stating otherwise; on your free attack after a successful trip, you should be able to make a melee attack as you desire. Your DM may rule it must be made with the weapon used to perform the trip.
As with iterative attacks, you have the potential with as many off-hand attacks to get a free trip attack, and the free melee attack with a successful trip. Keep in mind, some DM's may utilize the off-hand strength "penalty" for your opposed strength check with those off-hand trip attacks.
Ensure your off-hand weapon is either a tripping weapon, or an unarmed strike.
The only drawback, unless otherwise stated with certain feats, such as Rapidstrike, you can only make one attack per natural weapon in a round. Hence the entry for a wolf, one bite attack = one trip attack. Also note that if you have natural weapons, and a manufactured weapon, you can't make a natural attack with the same body part as the one holding the weapon, unless you are a monk using unarmed strikes. The natural attack, would be secondary attacks, and use the standard -5 penalty (-2 with Multiattack/-0 with Improved Multiattack).
This penalty applies even when the creature makes a single attack with the secondary weapon as part of the attack action or as an attack of opportunity.
Most natural weapons should count unarmed strikes for the purpose of trip attacks. A tentacle could wrap around a leg and pull a person off their feet. A claw can just as easily as a hand hook into someone and pull them off their feet. A bite, as in the case of the wolf, can drag a person off their feet. Speak with your DM ahead of time before trying to argue why your wing buffet should be allowed to trip someone.
Of course, with the knock-down feat, you aren't actually tripping them, you are doing so much damage in the right area, they are literally getting knocked down.
Attacks of Opportunity
Since a trip, is an attack, your attacks of opportunity can be made as trip attacks. For example, if you have a reach weapon or the Hold the Line feat, and an opponent charges you, you can trip him - possibly ending his charge before he gets a chance to hit you. Remember, attacks of opportunity happens before the action that provided the opportunity.
If you have the ability to make more than one attack of opportunity, such as Combat Reflexes, then you can possibly trip melee opponents with those attacks of opportunity, and also getting your free melee attack from a successful trip.
Is it Cheese?
Yes and no. If it is truly a problem for your encounters, start making the enemies larger and stronger. Also, lots of things can't be tripped or have a hard time being tripped. An angry centaur - gets a bonus for being large, and gets a bonus for having more than two legs. Oozes can't be tripped. Beholders... 'nuff said.
Remember this concerning what was stated above:
You Cannot Trip a Prone Target
All About Trip Attacks (Part Two)
It's possible to attempt a trip attack as an attack of opportunity. Fortunately, you can't be tripped while getting up from prone, at least not through the attack of opportunity you provoke. That because attacks of opportunity are resolved before the actions that provoke them (there are a few exceptions, see Rules of the Game: All About Attacks of Opportunity for details). When you try to stand up from a prone position, the attack of opportunity comes before you get back on your feet. Since you're still prone when the attack comes, the attack of opportunity can't trip you.
A tripped character is prone. Standing up is a move action.
The character is on the ground. Standing up is a move-equivalent action that provokes an attack of opportunity.
Attack of Opportunity
If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn).
A tripped character is prone. A prone character is on the ground, that needs to stand up. It provokes an attack of opportunity, unless you have feats, skill tricks, spells, or magic items that say otherwise. Since an attack of opportunity happens before the prone character stands up, he can't be tripped (caused prone) because he is still prone.
This was clarified in the Rules of the Game section, that is now archived on WotC website.
Being tripped makes you prone. Who can be tripped? Beholders? Gelatinous cubes? What effect does tripping have on these creatures? Can a prone character be tripped again? What about flying and swimming creatures? Many creatures have neither legs nor any relationship to the ground or gravity. How does tripping affect them?
Anything using limbs for locomotion can be tripped. Things that don’t need limbs for locomotion can’t be tripped. You can’t trip a snake, a beholder, or a gelatinous cube. You won’t find this in the rules, but then it really doesn’t need to be in there—the rules can leave some things to the DM’s common sense.
A creature flying with wings can be “tripped,” in which case the creature stalls (see Tactical Aerial Movement on page 20 of the Dungeon Master’s Guide). You can’t make an
incorporeal creature fall down. You also can’t trip a prone creature.
Creatures can’t be tripped when they’re swimming (the water holds them up). Likewise, a burrowing creature is driving its body through a fairly solid medium that serves to hold it up.
Are FAQ's Rules?
If you have a question about the D&D game rules, you might find them within this FAQ. Any new additions or major corrections in a version are provided in red text for your convenience. Red text changes to black text in the next version. This version of the D&D FAQ uses the 3.5 revision of the core rules and also contains questions covering material from a variety of books (such as Savage Species and Epic Level Handbook). If you haven’t yet adopted the revision, don’t worry—in the rare instance that the answer is different between 3rd edition and the 3.5 revision, we’ll bring it to your attention with a call out that says “Revision Alert.”
Are they factual rules? WotC seem to think so.
- All About Trip Attacks (Part Two)
- D&D FAQ 3/14/08 Page 68