Maybe Mylenium knows the 1337 way to do this, but a quick work around is precomposing the layer. Then take the precomp and scoot it up or down.
BTW parenting layers to nodes, then setting the keyframes in the nodes helps also.
You say that you tried something that you found in Help, but it didn't work. What, exactly, did you try?
Here's what I would recommend, from "Change multiple keyframe values at once":
"If you change a value by dragging the underlined value, all selected keyframes change by the same amount. In other words, you make a relative change. For example, if you select several Position keyframes on a motion path and drag the underlined value for one of them, all selected keyframe values change by the same amount."
From your initial description of your problem, it doesn't seem that you selected the keyframes themselves; it just seems that you selected the property.
I think Todd has the right tip - select the keyframes instead of the property. Since position values are an array, the context of the selection may not be able to get this right by just selecting the property.
Sounds like your problem is you're trying to move keyframe values when your current-time-indicator isn't situated on top of a keyframe.
So, first create a position keyframe, then select all, then adjust values to change all. (You should be able to delete the keyframe you created, but be aware it might change your fcurves, so double check they're correct after you delete.
Also, if I want to adjust a keyframes value when my cti isn't parked on it, I'll copy/paste that keyframe, select both keyframes, adjust, then delete duplicate.
Todd- yes, that's exactly what I tried earlier.
Here's a little more about the problem. In one comp, I have a layer with several position keyframes with different values. When I click "Position", all the keyframes light up yellow. I then drag the layer in the comp monitor window, but it doesn't change all the keyframes relatively- it makes a new keyframe (or just updates the keyframe that the current-time indicator is over).
HOWEVER, in this same project, in a different comp, I have another layer that I have applied tracker position keyframes to (and also several extra keyframes before and after the tracking keyframes). In this case, the relative keyframe change method works! (Clicking Position to select all, then draggint the layer in the monitor window.)
Why does this trick work in one comp and not the other?
Thanks again for your help!
Please reread my reply. Your problem is that you're trying to move the keyframes when you aren't situated on top of a position keyframe. Either move current time to a keyframe (j and k move to keyframe on left/right) and then adjust them, or create a new keyframe at current time, select all, then adjust.
Reason it worked on tracked layer is you have keyframes on every frame. Side issue: you should always track to a null and then parent your layer to that null.
I think that David's nailed it. (Of course.)