Next upgrade to an entry-level system?

As others have said, the phono preamp is a good call for your next step.  I think you should spend time listening to and reading about equipment.  Find a local high-end hi-fi shop and understand what brands are available.  

You don’t mention a budget.  You’re better off buying used, high-quality components piece-by-piece than run-of-the-mill stuff.  For <$5k, I built you a serious system that you could live with for a very long time and likely be happy: 

Audible Illusions 3A Preamp -  $1300 (This is a great Class A, dual-mono preamp) includes a phono section.

Jeff Rowland 112 Amp             $2399 150‑watt‑per‑channel stereo power amplifier, machined from a solid block of aluminum.  Made in USA

Moon  LP5.3 phonostage          $721 (widely regarded as one of the best sub‑$2k phono stages ever) - You don’t need this, the preamp includes a phono section. 

ITC-1 Speaker                          $495 (a boutique, engineering‑driven design with an external equalizer and unusually advanced crossover)

GRAND TOTAL                        $4915 

You already have a turntable so, I excluded it.  Use the leftover $85 to build your own speaker cable. 

(An alternate honorable mention speaker is the classic Dahlquist DQ 10 - but it went over my suggested $5k budget @ $699)

Audible Illusions 3A Preamp -$1300 https://tmraudio.com/fresh-arrivals/audible-illusions-modulus-3a-stereo-tube-preamplifier-mm-mc-phono/

Jeff Rowland Amp https://tmraudio.com/fresh-arrivals/jeff-rowland-design-model-112-stereo-power-amplifier/ $2399

Moon by Simaudio LP5.3 phono preamp $721 - https://tmraudio.com/fresh-arrivals/moon-by-simaudio-lp5-3-mm-mc-phono-preamplifier/

ITC-1 Speaker ($495) - Very Efficient w/killer sound  sound https://www.ebay.com/itm/177269994947?_skw=itc-1&itmmeta=01KDM1XXVVPQV06298ZWTQ8D2X&hash=item29461d75c3:g:~3oAAeSwtixod-PR&itmprp=enc%3AAQAKAAAA4FkggFvd1GGDu0w3yXCmi1eBjoqJrhIXWn%2FkCXoj%2FeMVXiaBUax6YIHbd6O%2FiKp4PH64%2BO6WmP7kGn1Tk2UMcK1rq7P6DsnFptkFrY1PQowZXrWVndarDf1BPZa7BPg8tVCzELTwhdRhLChGmYZN8WXjEO5atscMX5ZBExo5k0juDtSi36sO%2Bso%2B20flov0%2Fl5iN%2FnTGrPon3ZcXWTBTi8snBOIhuz97RESXo70JyBetZudQpEX4sE4Y1acMrYW7qt8N5aBjdFFWrbYqfL8O4WZ%2F9CMsiNumzJg0z1onwtzM%7Ctkp%3ABk9SR47e94HtZg

Alternate Speaker - Dahlquist DQ-10 ($699)  https://www.ebay.com/itm/357915612315?_skw=dq-10&itmmeta=01KDM1T2XYDNAWJXV6W2YZ92B2&hash=item53556ed49b:g:u0gAAeSwPJRpG4lJ&itmprp=enc%3AAQAKAAAAwFkggFvd1GGDu0w3yXCmi1efJzv04bO0Os%2BaNLBdFzjPTuqM8E3%2BvESssTEYD%2BFBPq7NgMk3%2BSeeVjS6G8ZOS5eD%2FeKwKWs%2BZNsSr5%2FdGfbDDMrokzqxrAo5qb6JmLzbV8N30929f%2BX0eH1mSFbMLCOQhMC0HPb4cdln3cb3srNcslSBrfF5q87gxriVZEW7%2BmGtRhnbnRIJIbVwMNTls5iGAIMkoKb0%2BDEp%2BZCW2MQ7sX0Ku%2BRDuXfPkjpSkPnPeg%3D%3D%7Ctkp%3ABk9SR46v6IHtZg

@saintsaens_op61 

Above all I would concentrate on the front end first. Your amp and what it sends to the speakers is only as good as what you feed it. May I suggest https://www.musicdirect.com/equipment/turntables/rega-planar-3-rs-edition-turntable/ and https://www.musicdirect.com/equipment/phono-preamps/rega-fono-mm-mk5-phono-preamplifier/? This would be an absolutely stunning improvement. Gift the AT to somebody you know just starting out!

Your amp and speakers, at their price point have been well regarded for years. Though I wouldn’t consider them the most compatible you can live with them in the meantime while you recover from the shock of the above purchase I recommended. Then you can think about changing out the amp or speakers to achieve a more sonically compatible combo. If it works for you can stay with that for as long as it satisfies you or go from there.

If you really enjoy the vinyl thing and collecting new and used records, invest in some inexpensive maintenance tools like a Spin Clean for the used records you pick up at your local haunts along with a good carbon fiber brush and silicon roller for daily maintenance before playback and a good, densely pack carbon fiber brush plus a good quality stylus cleaning fluid which is expensive but lasts along time that will eliminate any distortion caused by residue on the stylus. I use LAST and one of their brushes before every play. Include always having good inner sleeves on hand. I use Mofi because they’re easy to find and economical and I get a 100 pack of Acoustic Sounds 3 mil outer sleeves for $20 and re-sleave everything. If your original inner sleeves have valuable information regarding album content or advertising etc., from the original publisher keep them tucked inside the original outer sleeve to maintain authenticity. You’ll appreciate that later and you’ll probably be listening to the same record for the rest of your life.

When you get the urge you can splurge on audio jewelry like interconnects, power cords or speaker cables and see if that does anything for ya. You can always lavish accoutrements on your system like you would a pet if the spirit moves you. Keeps it fresh.

No  mention of line conditioner, or cables , Wireworld  Eclipse 10, or Equinox 10 which is less expensive , both excellent value in their respective class .and a Quality aftermarket power cord is essential ,what are you plugging equipment into?

no digital ? 

As for loudspeakers you need to step it up  maybe the Newer Sonus Faber Sonetto G2  line lots of buyers was on back order for a year , that says a lot . Your loosing 

a ton of potential in sonics speakers and source are critical , cables carry the signal 

that too cannot be over looked.

The OP can spend $150 for a  user review positive, inexpensive sonic upgrade or we can start a GoFundMe account to raise enough to cover everything under the sun suggested, which adds up to a complete setup.

saintsaens_op61 probably knows it's the sum of everything to complete the picture.

Long game would be speakers, which starts the wallet emptying game. The OP's setup suggests simple and just listen to nice LP's?

Speaker/sub setup/location and optimization is a game changer and free IF your space allows.

Happy New Year's listening.