flexographic printing is a spot color process.
Each color is a separate ink and not made by mixing process colors.
It is a very course printing process with loose color registration.
I see approximately six or seven colors plus tints (percentages of spot color) in your character art.
The example with die line seems to be best compromise to use only 4 colors.

Full process four color printing would require a coated paper surface (maybe a large label) on your pizza box, an unheard of expense.

I am not sure what can be done beyond what you already have...

Can the words “Pizzaria Romana” font be changed or I’d thst apart of your logo?

can you guarantee the payment, thanks

Hi,
I have submitted a design for your project. Please provide me with a private feedback.
Thanks!