What kinds of effects can modify a die roll?

Question

After you roll a d20, there are some effects that can modify the result before the calculation is made. Is this a complete list?

• If you don't like the roll (before you know success or failure), throw it away and roll it again
• If you don't like the roll (after you know the result), throw it away and roll it again
• Roll it again and take the better result (oath of enmity)
• Roll it again and take the worse result (various curses)
• replace a die roll with one you rolled before (dice of auspicious fortune)
• add a number to the die roll (heroic effort, adept's insight)

And I think these only apply to a damage roll:

• Brutal
  • if it's N or below, re-roll until it's N+1 or above
• if it's N or below, throw away the old roll and re-roll once, taking the result no matter what
• if it's N or below, change to N+1
• if it's the maximum value, roll again once and take the sum
• if it's the maximum value, roll again, take the sum, and repeat if it's maximum value (vorpal/explosive)

Answer 1

Don't know if you count these into one or more of your bullet points, but...

• Add another die roll to the die roll (Memory of a Thousand Lifetimes^[DDI]).
• Replace the die roll with a fixed number (Climatic Crescendo^[DDI], if you consider the critical hit a natural 20, which could be a bit over-reading it).

Answer 2

Brutal N is re-roll until you get N+1.

Certain features allow you to a roll a d20 ahead of time and save it, then replace a later roll with the result of the saved roll if you want.