Do you mean half pullout and half door? You would have to hack it. Two immediate possibilities come to mind, not that either would work. You would just have to buy something and start from scratch. You might end up with nothing and be out the cost of the bases.

A 30" sink base with a custom divider at the bottom high enough to mount the inner slide for the pullout.

Two 15" bases with them cut out in the middle and fitted for the sink.

You need to keep the drain line(s) in mind while you are doing all this. Type of sink, countertop, etc. all need to be kept in mind too.

Good luck. If you try anything, successfully or not, please post back what happened.

Yes, you would have to hack it. Like doug said, keep the details in mind when you do this - the drain for example probably cannot be dead center in the cabinet because it would interfere with the drawer - you would then need a right or left drain sink, so the drain would be off to the side

I would think you should be able to use a 15" wide IKEA tall drawer. You simply would have to attach a 4x4 or similar to the bottom of your 30" cabinet for the other drawer slide to connect to. It won't be the prettiest when you open your cabinet, but it would work. Or, you can always paint it to match the cabinet.

You could instead buy something like this and install it in the IKEA cabinet. Be careful when you drill through the IKEA door - the screws provided should be short enough that they won't go through the front of the door, but be sure to double check. http://www.homedepot.com/p/Rev-A-Shelf-Double-27-Quart-Waste-Containers-RV-15PB-2-S/202855941?N=5yc1vZc3uk