Bitting up a horse means to use increasingly harsher, and harsher bits to get a desired effect.
A kimberwick, a twisted snaffle, and a hackamore are all "stronger" bits. And before it is stated that a hackamore isn't even strong, have you seen the length of those shanks? The amount of pressure per pound in the hands can range from very mild... to very harsh.
A horse may not like multiple moving parts in a bit. A mullen might solve that, but if he needs tongue relief, a solid bit that is not harsh in green rider's hands might help. I personally know of a mustang whose bitting problems were solved by switching to a simple solid curb.