" Another phono stage may or may not offer any significant improvement. Also, upgrades seldom result in huge leaps in performance but rather smaller, incremental steps. Its this last 5% in performance that we all seem to seek. So more info would really be needed to give you any kind of meaningful answer."
Not with vinyl. You could make a better case with digital, but for records, upgrading from entry level equipment can offer huge leaps in sound quality.
"Curious what if anything I would gain by adding a phono preamp? Am I understanding correctly that this integrated model has a preamp already built-in?"
If you are currently listening to records, then you have a phono preamp. It doesn't work any other way. When you upgrade, though, you have to be careful. Not every phono preamp works with every cartridge. You need to do some research on the different types of products that are available. The differences between moving coil and moving magnet cartridges are important, as well as how to match them to a phono stage. Its not difficult material to learn, but you do need to know it before you proceed. Normally, I don't recommend magazine reviews because the info they give you can hurt as much as help, but it wouldn't be a bad idea to read some reviews on analog gear. After a little reading, you should start to get a feel for how the different pieces go together.