Is it possible to increase the number of times an object is drawn on screen so that I can smooth out the appearance of fast moving objects?
The engine doesn’t actually draw each object separately. It draws the entire scene, so that things like lighting and occlusion can be taken into account. In order to redraw an object, you would need to redraw the scene. By default, the engine already does this as fast as it can, with one exception that is the V-Sync.
V-Sync causes the framerate to not exceed the monitor refresh rate, but that’s usually a fairly high limit, such as 60 frames per second. Any further framerate increase would be very difficult to notice, because both the monitor’s ability to display new frames and human eye’s ability to see them are limited.
When you play commercial games, you can sometimes notice various graphic effects, such as blurring, swords being followed by a visible trail, or an object being drawn in several places at the same time (this is achieved by having more than one instance of that object’s model). These tricks help to create the illusion of smooth movement when the object is actually moving so fast that we wouldn’t normally be able to see it.
Another trick in use is to have separate “frames” for actual display and for physics calculations. Display happens as fast as it can, which may sometimes be not very fast. But physics are calculated at a fixed rate, so that movement and such are not affected by the framerate. Unity does support that. In order to do your movement calculations at a constant rate, put the movement code in FixedUpdate() instead of Update(). The rate of fixed updates is a parameter that can be changed in project settings.