Help Pricing an upgraded item.

[Childeric, The Shatterer]

Let's say I want to upgrade a Cape of the Mountebank to be usable 3 times per day instead of only once. How would I determine the price of the upgraded item?

Cape of the Mountebank
Aura moderate conjuration; CL 9th
Slot shoulders; Price 10,800 gp; Weight 1 lb.
Description
On command, this bright red and gold cape allows the wearer to use the magic of the dimension door spell once per day. When he disappears, he leaves behind a cloud of smoke, appearing in a similar fashion at his destination.
Construction
Requirements Craft Wondrous Item, dimension door; Cost 5,400 gp

[Dark Lord Fluffy]

Honestly the pricing on that is a little off formula for its caster level, but there shouldn't be any harm in just tripling the cost going by the charges per day rule.

[Dastis]

Considering you can take it off and put on a new one, just triple the price

[Childeric, The Shatterer]

Dastis wrote:

Considering you can take it off and put on a new one, just triple the price

That was my Initial though as well, but I'm not DMing in this game and was hoping for a more official (or at least web-supported) way to price it to show the DM instead of an arbitrary number.

[Dark Lord Fluffy]

Childeric, The Shatterer wrote:

That was my Initial though as well, but I'm not DMing in this game and was hoping for a more official (or at least web-supported) way to price it to show the DM instead of an arbitrary number.

In this case it is not arbitrary. There is a rule for magic item pricing regarding charges per day. Each charge is worth 1/5 the cost of an the 'unlimited' price. Of course some items should never exist as unlimited. Since this item has no attunement and has no other abilities other then the single charge of dimension door, using the charge per day scale seems appropriate. You could look at boots of teleportation as an example item with a similar effect and multiple charges. It is just shy of 50k and grants teleport 3/day.