I'm in a tight spot. I've done this before while replacing the sill and rim joist. But this time I've got no room to get a bottle jack in between pier and beam. I've poured several piers for the sill beams (6x6) to sit on (the old ones deteriorated), but I only have about 5-6" in between the pier and the beam that needs the lifting.

In the past I had a couple of feet to do it with a 20 ton jack. This time I need another trick. I have to do this 5 times to get something solid under the beams (5 piers).

Man, some pics would really help. I'm having a hard time visualizing what you are saying.

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ETA: After rereading what you said, could you dig a hole next to the pier deep enough to get your jack in there?

I could. I'd have to have some way to keep the jack from sinking instead of lifting the house, so it might take another pier that gets covered back up later.

I may be missing something here, but why would your pier be above the frost line?

It's not.

I agree. Time to dig and pour a secondary pier hole deep enough to get your first bottle jack operational under the main beam. Then you can use the height gained by the first jack to use existing piers and more jacks.