For the purpose of this article, each combo described will be the crux of a pretty standard Hunting Party engine; the deck in most of these cases should be built exactly to the same specs: 1-3 Silver, 1 Gold, 1 linchpin card and as many Hunting Parties as can be massed in time to end the game in a win. The linchpin can be described as any Kingdom card that is not a terminal draw or cycle card. These terminals will completely disrupt a Hunting Party engine and should be avoided.
<b>Hunting Party/Horse Traders</b>
Horse Traders is an excellent focus of a Hunting Party engine for two reasons: first of all it can help a lot to get the $5 needed to buy early Hunting Parties, and secondly it gives $2 and a buy once the engine is firing. Any $2 terminal can be used in a Hunting Party deck. Militia, Swindler etc can all be used to success but I feel that Horse Traders is a cut above the standard for the help it gives in getting the engine rolling in the early game.
<b>Hunting Party/Scheme/X</b>
Adding a scheme or two to a Hunting Party deck is pure love. The deck can handle the Schemes rather well, and as a rule I never add extra engine cards to this style of deck. Scheme is the exception. I like to play the Schemes as soon as they appear, before continuing the chain. With two Schemes in a focused deck it is pretty much a given that each turn will begin with two Hunting Party plays.
<b>Hunting Party/Secret Chamber</b>
Typically, a Hunting Party deck can stall once too many victory cards have been added. For this reason I try to avoid Duchies as long as I can get away with it. Duchies cause a flagging Hunting Party deck to die. Secret Chamber transforms a handful of useless greens into cash.
<b>Hunting Party/Mandarin</b>
I do not know how great this is opening 3/4, but with 5/2 it is awesomeness incarnate. Buy the Mandarin, put the $5 back on top and buy the Hunting Party. The really nice thing about this combo is that once the deck has generated enough cash to Province you can use Mandarin to put an extra Hunting Party on top of the deck for a jump start on the next turn. This is a very fast deck unless some serious bad luck occurs.
<b>Hunting Party/Haggler</b>
I have found this to be about the sweetest card to play with Hunting Party. On the typical late turn chain up to $6 + Haggler, buy a Province and gain an extra Hunting Party. This jolt of power will keep the deck running strong all the way to the end.