Yes, can get a separate pre/multi-channel processor, but then need a multi-channel amp. But, for a very nice set-up like that you could easily exceed your $1,000 budget. There are some good ‘higher end’ companies that make these kind of products. The newer ones may also have streaming integrated within, and an integrated DAC.
But, as a starting point, as mentioned above, I think your best solution starting out may be a higher end AV receiver.I was in the same boat years ago, purchased a higher end Yamaha AV receiver (before realizing I was going to get serious about music again), and some may frown on this here, still use it as my pre-amp; in a way. It has 2 channel pre outs for a separate amplifier, so now my front main speakers are being supplied power directly through a much nicer power amp for dedicated stereo listening. I also added a separate and much better DAC (Than in my receiver and other components) that supplies direct input into my receiver and ultimately thru to my 2 channel amp, and both my CD player and streaming ( actually simply a little wireless ‘connector’) box runs through the DAC. This has made my CD/blue ray player just a transport when playing dedicated 2 channel stereo when I’m critical listening, same with streaming, mainly thru Tidal via my iPad, or via my music files on a exterior hard drive connected to my wireless router. I also have purchased a dedicated phono stage instead of using the built-in phono stage in the receiver when playing vinyl, which I am doing more and more lately. Basically, in the end, I’ve turned my receiver into an RCA stereo ‘pass-thru’ for all my other components that does sound better than the receiver. As a last touch, I added a very neat (but not cheap) Ifi tube buffer/pre between my receiver and my 2 channel amp to warm things up and add some great options sound-wise to dedicated 2 channel listening, and to make up for a lack of a good dedicated preamp which does add a lot to a 2 channel set-up. My goal, as I went along, was to eliminate all and any 2 channel listening via HDMI for a better analog experience when listening to music.
So, a good AV receiver can become a ‘base’ you can add to as your ears want, need, or require, for 2 channel listening, but also work as your home theater component as I also use mine, (as I do not have a separate and dedicated stereo listening room). I now have a very nice 5.1 home theater set-up for watching TV/ movies, but with a little ‘switching’ via my AV receiver app, can turn it into a very nice 2-channel system when critically listening to music, which I do daily. And you can add to it, or not, which is why if you go with the AV receiver route, start with a good one.