What improvements would I get with a "better" preamp?

If you really like the sound of the 2ASE,  have you thought of checking out the 2BSE?   Or how about the Line 2CRM?
I currently have a PS Audio BHK Signature preamp. I switched the input tubes and have been really pleased.  FYI, they just stopped making the and they are currently selling at half price, and can be found for around 3K used.

On phenomenon about the use of AI instead of forums to obtain answers is that it diminishes the library of information AI pulls from to generate its answers.   When we ask AI how a speaker sounds or its characteristics, AI, which can't hear, pulls from forums like this to develop its answers.  While it's true that it can 'see' test charts, it does struggle translating a peak at 4 kHZ into how that sounds to us, particularly when paired with particular electronics that were not used in the test charts.  

@curiousjim   I have the BHK pre as well and really like it.  I think there are benefits to having a tube front end, with a SS output stage.  I am focused on room treatment next, which is very complicated since I know nothing about that aspect of audio unlike electronics.  My next upgrade may be the preamp, so this thread is great, but not sure any move I make would be any more than a sideways move.  

Someone ask the AI engine what hifi combo it thinks sounds the best and how much it should cost.

I dare ya!

I wasn't a big proponent of changing preamp vs power amp. I thought power amp will give you bigger improvement over preamp. This was until I put my new preamp in the system. I am not exaggerating, but it was a WOW! Everything improved. I've got bigger soundstage, more details and less grainy sound. I completely agree with @patrickdowns. Improved immediacy and dynamics. Improved imaging. In my case live and natural representation, the feeling like you are in front of  musicians or like you are in the studio. Music became more airy and easy flowing. I sat and listened for hours and I was re-discovering music I know by heart. Of coarse I am talking about tube preamps. Design is very important. Don't go for preamp with many tubes involved. This is a wrong understanding than the more is better. It is quite opposite. Look for good sounding tubes, capacitor-less design and high quality parts. High quality parts are bringing the refinement and microdetails in the sound. They can shape the sound too. They require longer brake in time, but the improvement is worth. In short a good preamp can bring big improvements if chosen wright.