How far down the Presidential Line of Succession can you get w/o cheating?

For those not in the know the Presidential Line of Succession is the line that is followed down the political hierarchy in naming a replacement to the President of the United States should he die, resign, become incapacitated, etc. For example, if the President dies the vice President is the first in the line of succession to replace him as sitting president. The Vice President is also the only person in the line of succession who will serve out the remainder of the original presidents term if he is put into place. Every person beyond the Vice President is an “acting president” and elections must be held by December of that year, or December of the next year if it is within 2 months of December.

I thought I knew it down to the 4th person, but I was incorrect after the Vice President. It is worth noting that the Line of Succession has changed a few times in the last 200 years, most recently in 1947.

Without cheating, how far down the Presidential Line of Succession can you get. We want the political position not the current person filling it. For example if you think the 4th person in the line of succession is the minority leader of the House of Representatives, you would say the Minority Leader in the House not Nancy Pelosi.