I think you would still be using the onboard headphone amp if you used an outboard amp to further increase the amplification of the headphones. Unless you have difficult headphones to drive, I don't feel this would be beneficial.
I found that a dedicated headphone amp was a real eye opener using AKG 701s. This was a home based amp- OTL using 6080 NOS output tubes and one of my better 6SN7s as an input. It was not exactly cheap around $1500- But WOW what a difference. I refrain from suggesting the amp because the owner has been discredited, but his product if one of his good ones was amazing.