S.H.
I had that once.
My hair is very thick (meaning I have LOTS of hair AND it is thick with a slight wave). But it was not layered.... my hair was all one length & shoulder length.
It was a real cute 'coil' type perm... lasted a LONG time... and I got many compliments on it.
For my perm.... some strands were coil permed, and some strands were left as is... meaning, straight and untouched by the perm. So, I had a real funky alternative look... and perm. Which is what I wanted... and which the Stylist did for me, per MY looks/style of personality.
It was real cool.
My hair, did not ever get all "poofy" or unmanageable or messy looking. It was a good, perm.
And yes, they can perm it, excluding the roots.
Just bring a photo with you, of it and what you mean.
As for products afterwards, I did NOT use hair products on my hair after the perm. I didn't have to.
I just used a gentle shampoo and a conditioner.
As I said, like you, my hair is THICK, slightly wavy, can get frizzy, and I have LOTS of hair too. My coil perm was fine.
The Stylist, used the appropriate perm solution....
In my State, there is humidity. My perm was fine. It did not get all wigged out due to humidity.
Because your hair is layered though... I don't know... how the coil perm will turn out. Ask the Stylist..... it will probably be/get real "full" looking... due to the layers in your hair....
all the best,
Susan