I've done this many times. I like to create layers of soap with old soap and sometimes new soap over some days.
There are a couple of ways to help layers of older soap adhere to the new soap better. You can score the older soap (sort of like if you were scoring a peanut butter cookie prior to baking the cookies). The rough scoring helps the new soap have something 'grab onto' as opposed to just sitting on top.
If you want the layers to be totally flush, though you can get the dry older layer wet first to soften the top surface (make soap glue - get soap wet and a tad mushy like paste, and smear it onto the dry soap). Then be sure to CPOP. The CPOP will help the layers to adhere. This is much like 'soap welding' which works to stick pieces of soap together, but may require an extra step (see next paragraph.)
If layers start to separate when or after you cut the soap you can complete the weld this way: Get the layers wet, stick them together, wrap the bars in plastic kitchen wrap very tightly, place in oven and heat. Here are links for more information about this process:
https://www.soapmakingforum.com/threads/smf-july-2020-challenge-welded-soap.79925/For more links, see the first post in that thread for an ebook and videos showing the process.
I think the plastic wrap idea that I use is not covered elsewhere, but it works fantastically and I have not had welded soap fall apart using this method (thoughout the life of the soap in use).
Another way to 'weld' the soap that I think DeeAnna uses for curing partial gel also works to 'weld' non-sticking layers, as long as you wet the non-adhering surfaces first. That is to put all the cut bars back into the original mold and heat the soap in an oven. I would follow the same procedure for heat & time that I use when made the welded soap in the first linked post above (200° F for about 10-20 minutes,
@bookreader451 found 40 minutes worked better for her, so it could take longer, for whatever reason).
One tip that works for me: If you know ahead of time you won't be able to put all the layers together on the same day, wrap the soap in plastic wrap to slow down moisture loss. The adherence of each layer is much more reliable for me when I do this. I have used soap as old as 18 months in layers this way and had no problem with the layers sticking together.