Because you asked for something similar to your River, I may have the perfect answer for you. Depending on what weight/plastic your River is, you might be able to fill this slot with another River.
160-168g weight Rivers in Gold Line Plastic are understable new, or beat in very quickly. 170+ Rivers are very Eagle/Teebird like. I throw 350' golf D, and have to get 100% power behind my 175g River to get it to turn over at all.
If your current River is too understable, buy one in the same plastic, but 5-6 grams heavier. It'll stabilize it quite a bit.
If you want to try something other than the River, here are the most popular options:
Teebird: straightest, most reliable driver ever made. A perferct compliment to the River. But unless you're throwing 400' or more, a new Teebird in Star or Champion plastic will act overstable for you. After it beats in, it'll be money. If you want to try a driver that's a lot like a beat in Teebird, a Champion TL (discgolfvalues.com has CAL Champion TLs that are great.)
Eagle: There are two different discs that fall under the Eagle name. The Eagle-X and the Eagle-L. X being more overstable than the L. The Eagle has less HSS than the Teebird, so if you tend to put a slight hyzer on your drives, the Eagle will flip to flat, where a new Teebird will tend to hold that hyzer angle. A max weight River will mimic the stability of an Eagle in a lot of ways. So the Teebird may be the better option if you want to avoid overlap.
Z/Glow Stalker: Not as long as the Teebird, Eagle or River (for me) but dead-nuts straight once you learn how to throw it. Handles low-ceiling shots exceptionally well. The issue with a Stalker/River combo is that neither disc handles headwinds very well. The Teebird handles better into headwinds, especially in the premium plastics (Champ, Star, Glow, etc.)
PD (Freak): All of the good things about a Teebird, but longer. The worst thing about PDs is that, unless you have a decent store near you that carries it (it's made by Innova's Euro branch) you'll have to risk ordering it online. If you do that, find a store that you can order over the phone, and request a flat PD. The higher the dome, the more overstable. And when I say overstable, I mean OVERSTABLE. You'll notice it comes in "P" plastic (which is Innova Pro plastic) or "S" plastic (Star). For your first PD, I'd recommend a 170g in P plastic. If you've not broken the 350' barrier yet, try one in the 164-167g range.
Striker: Great disc. In a way, where the PD is a longer Teebird, the Striker is a longer Eagle. The issue with Strikers is similar to the PD, but worse. Some are domey, some flat, some overstable, some stable, and some understable. And unless you have a store near you that carries Lat64, you'll be trying to explain PLH (parting line height) to a guy on a website over the phone.
Because I don't know what you power level is, I'll say this. If you throw:
250' - DX 170g Teebird
300' - Star/Champion TL, Eagle-L or Z Stalker
Above 300', you'll be able to control any of the other discs. But who are you kidding, you're going to eventually try all of them anyway!
