99 Grand Prix Shakes

I have a 99 GT that has run flawlessly for 85,000 miles.
In the last three months, about once a month when I start the car it will shake. If I give it a little gas the car will stop shaking and then run fine. This happens when the engine is cold and also after it has been driven.
Last week when I started it up it shook so bad I shut it off after about 3 seconds. After turning it back on it was fine.
Any ideas as to what this might be? I am obviously out of warranty and unfortunatley I do not have a dealer I trust.
As a side note: I used to drive a 99 Intrigue w/ 3.8 (the 99GP was my wifes car...she now has a 03 Envoy XL SLT). My Intrigue did the 'shake' three or four times in the last year I owned it. Seems like it might be something others have run into with the 3.8 Series II.
In the last three months, about once a month when I start the car it will shake. If I give it a little gas the car will stop shaking and then run fine. This happens when the engine is cold and also after it has been driven.
Last week when I started it up it shook so bad I shut it off after about 3 seconds. After turning it back on it was fine.
Any ideas as to what this might be? I am obviously out of warranty and unfortunatley I do not have a dealer I trust.
As a side note: I used to drive a 99 Intrigue w/ 3.8 (the 99GP was my wifes car...she now has a 03 Envoy XL SLT). My Intrigue did the 'shake' three or four times in the last year I owned it. Seems like it might be something others have run into with the 3.8 Series II.
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Comments
This is cross-posted in the GP forum...
I don't know much about car engines, but oil getting on the plug makes sense. I've had my lawn mower have that happen and cleaning the plug fixed the issue. The car usually only shakes for 2-3 seconds, which is probably enough time to burn off any oil.
As the rings/seals wear more and more start up/cruise oil is sucked into the cylinders under vacuum. The plug change interval has to be adjusted downward to compensate.
But 85,000 miles is young if you have been changing the oil every 90 days. [small filters can't hold much dirt]. Check and clean PCV/EGR/plenum system to minimize additional dirt/oil.
Thanks for the advice.
Engine coolant flush
Trans fluid flush (which actually seems to have made it shift smooter...I wasn't expecting a change)
new belt
fuel filter
air filter
spark plugs
front brakes
brake fluid
I mentioned the occasional shaking to them. They said the plugs were pretty 'worn', but the wires looked fine. Their first guess was that the wires could have corroded and moisture was building up on one of the plugs.
They said it could be a number of other things, but since I can't reproduce the problem and it happens infrequently they suggested waiting to see if it still occurs. I agree with that, even though I am going to guess that the shakes will come back.