Yes, you can have both outlets on one circuit. Why would you think you couldn't?

The only issue is if operating all of that plus whatever else is in that circuit, will be too much for one of your GFCI protected kitchen small appliance circuits. What else does that circuit serve? ID the loads.

I am new to all this, plus I am a women who not supposed to know all the details:) that’s the answer to the question why I thought I couldn’t:) I am installing the Servo-Drive for my drawers in the island which need to be plugged in all the time. And in the outside I just want a regular outlet. Another question, I guess electrician who will do it for me will know. Does it have to be 2 separated electrical boxes or I can do a single outlet that can be plugged it from inside or outside? I haven’t seen outlet boxes like that but may be I don’t know. Thank you for your help, all.

Sorry if my question came across as me insinuating that it was a dumb question. I meant it more in the terms of "Did someone say you couldn't?" meaning that perhaps an electrician had told you something about this particular situation that could have changed my answer if I knew the details.

You'll need two boxes.

@User: "Your kitchen designer should have created the lighting and electrical plans. Consult with them."

This doesn't help the questioner.

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Do the following:

1. Locate the circuit breaker that protects the existing outlet. Turn that breaker off.
2. Turn on each light that may be connected to the circuit. If it no longer turns on, it's on the circuit.
3. Plug a lamp into each nearby outlet. If the lamp won't turn on, the outlet is on the circuit.
4. If you find an outlet that's part of the circuit, what's plugged into it? If it's a high-wattage appliance such as a toaster or microwave oven, then you may be limited to what you can plug into a new outlet and operate simultaneously. For example, you might not be able to operate a toaster and microwave at the same time without tripping the circuit breaker. If there are no high-wattage appliances, you'll be free to plug whatever you want into a new outlet anytime.

If this is a new build or will be subject to electrical inspection, the answer will differ. In the jurisdiction, I build in, all kitchen receptacles must be split, i.o.w. two separate circuits. Your licensed electrician will know the correct answer.

It’s nit a new built, so will be no inspection but of course I prefer to do it the right way:)

Yes it is possible. We split our island power into three outlets. Two are dedicated to small appliances and one extra for hand mixer, etc. Your electrician will know how.

Do you plan to put this new receptacle behind a drawer? Is there room for the drawer to close, or do you have to modify the drawer?

"plus I am a women who not supposed to know all the details:"

WHAT????

Being male or female has nothing WHATSOEVER to do with whether or not a person can, does, or is "supposed to", know the details. Anyone (just about) can learn anything. No one knows everything.

@catbuilder: "Being male or female has nothing WHATSOEVER to do..."

Oh calm down. It was a joke. She even put a :) after it.

Been a while since I got to this post! Thank you all for comments, not for the ones that comments on what I did or did not do, but I do see there are comments that are helping. Splitting one circuit live into 2 outlets. The reason I need it in the first place is one inside for the servo drive (Blum hardware that requires electricity) and second one for the outlet outside on the island. Thanks again all!

Is your servo drive going to be hard-wired, or are you going to have a plug-in receptacle behind the drawer for it?

@mtvhike I am planning to do a separate plug-in receptacle , it needs transformer I think so I will have a receptacle behind drawer to plug it in, or I can probably hardwire the transformer, not sure.

Your in-cabinet outlet may not be allowed on the same circuit as your island outlet - confirm with your electrician/local electrical inspector.