Attacking, you get an iterative attack every time your BAB increases enough that BAB -5x is still positive, ie, at +16 you also get +11, +6, and +1. Has to be done as a full-round action.
What if you let other skills be used this way, even mixed with each other? The two best examples I can think of are climb, and bluff (as a feint). One climb action lets you climb half your speed. If you had 6 ranks in climb, let them take a second climb at +1 instead of +6, to do it again. Once climb broke 16, they could climb up to double their speed as a full-round action, but it would take four checks of increasing difficulty.
Similarly, bluff-as-a-feint is a standard action. If you let it be mixed this way, and had bluff +12 and BAB +12, you might attack at +12, bluff at +7, and attack at +2. This is almost always suboptimal, because the attack at +7 would have usually worked better anyway, but might work for a rogue.
Improved feint would still be useful, since it would let you bluff once at full bonus and attack once at full bonus (as a move and then a standard action), where without the feat but with iterative actions, you could bluff at full bonus and attack at -5 as a full-round action.
This kind of thing would usually only come up in combat, so it would be limited to skills that get used in those situations. Don't know how it might apply to tumble, since that's usually done during a move anyway, not as a standard action or as part of one.
What if you let other skills be used this way, even mixed with each other? The two best examples I can think of are climb, and bluff (as a feint). One climb action lets you climb half your speed. If you had 6 ranks in climb, let them take a second climb at +1 instead of +6, to do it again. Once climb broke 16, they could climb up to double their speed as a full-round action, but it would take four checks of increasing difficulty.
Similarly, bluff-as-a-feint is a standard action. If you let it be mixed this way, and had bluff +12 and BAB +12, you might attack at +12, bluff at +7, and attack at +2. This is almost always suboptimal, because the attack at +7 would have usually worked better anyway, but might work for a rogue.
Improved feint would still be useful, since it would let you bluff once at full bonus and attack once at full bonus (as a move and then a standard action), where without the feat but with iterative actions, you could bluff at full bonus and attack at -5 as a full-round action.
This kind of thing would usually only come up in combat, so it would be limited to skills that get used in those situations. Don't know how it might apply to tumble, since that's usually done during a move anyway, not as a standard action or as part of one.