Turn clean out to drain

[Kwood]

Hi, I am adding a utility sink to my laundry room and I was wondering if I could just remove the cap on the clean out drain and add a wye fitting. Use one side as the clean out and the other as my drain.
My kitchen drain was done this way and I was hoping it would be simple. Would it need anything else?
I've attached the image of both the laundry room and kitchen sink drain.

 

[Terry]

You mean something like this?

 

[Sponsor]

 

[Kwood]

You mean something like this?

No, I meant splitting the clean out drain line. So in the image the red circle is my clean out drain, I was thinking of putting a wye fitting and using one side for my sink drain the other side for the clean out.
Like my second image, it is of my kitchen sink drain. So I would copy that.

If that wont work, can I connect to the washer standpipe, like your image? That was what I originally wanted to do but read in a few places it was a no no

Edit- this type of fitting

You mean something like this?