In a 1980 "Guns & Ammo" article on Sharps rifles, Elmer Keith reported that he was frequently asked what smokeless powder was best for the Sharps. Crusty old Elmer's reply was "NONE"! And then he went on to explain why the rifle was best served with black powder loads. He of course was referring to his experience with his seven original Sharps rifles, which he had used extensively for hunting.
Modern Sharps rifles are made with modern steel, which manufacturers claim is stronger. However, the basic action, which goes back to the Sharps Civil War rifle and carbine, is a black powder pressure design. While there are those who load cartridges to 40,000 psi and higher for their Sharps rifles, I prefer my black powder loads. After all, who am I to argue with old Elmer.
Factory 45-70 cartridges are loaded to around 1300 fps with 405 grain jacketed bullets. They are designed for lever action rifles with tubular magazines and have an overall length of 2.550 inches in order to function thru the action. You can do a lot better than this in your single shot Sharps. Your only OAL limitation is where the bullet engages the rifling in the throat of the chamber. Thus, longer and heavier bullets with a better ballistic coefficient can be used. Black Powder Silhouette shooters commonly use lead/tin allow bullets up to 550 grains for this long range competition, which of course limits powders to black or black substitute. Hunters also use these loads in their Sharps rifles to take big game up to and including buffalo. Frankly, I don't know why someone would need more than this.