When you are creating an Auto Relist profile you can deselect the checkbox for "Relist with no changes" and you will be able to lower the start price by percentage if you wish, this is in the same area where you can alter the duration or quantity using such a profile. If you have the profile set to relist if no items have sold, this would relist the item at a lesser price than the original posting if it did not sell.
There is no option at this time to increase the start price on relist, although you can set the profile to relist if any items have sold, there is no capability to have a single profile operate off of either possibility - it can be set for if "any items have sold", "all items have sold" or "no items have sold" but not under two of these circumstances. You would need to relist manually if you wished to increase the price of an item once the initial listing had ended.
However, I have forwarded your suggestions along in the form of a feature request to our Product Management team for their consideration.
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