@James K's answer, above, is correct (and I've upvoted it), but I'd like to expand on it more than comments allow.
Don't forget the inverse square law! The starlight light available to be reflected drops off with the square of the distance from the star to the reflector. Except for very close binaries the inverse square law dramatically diminishes the total amount of reflected light.
There's a simple way to work it out: All the light from a star passes through the sphere centered on the Sun with a radius of the Earth's orbital distance. (The Earth's orbit can be thought of as the equator of that sphere.) The only light Earth can reflect is the tiny part its surface intercepts. The rest streams past it into space.
If r is the Earth's radius and R is the radius of its orbit, the fraction intercepted and available to be reflected is (r/2R)2. With 4=4000 miles and R=93,000,000 miles, that's just a bit over 4*10-10 of the Sun's light is available to be reflected by the Earth. (Earth reflects most of it.) If you do the arithmetic, Mercury, Venus, Jupiter and Saturn roughly the same and the rest of the planets make a pretty minor contribution. The total reflected (before albedo losses!) is around 4*10-9 of the Sun's light.
A closer-in planetary system will reflect a bigger proportion of the central star's light -- it scales as the inverse square, of course. If the solar system were ten times as compact but the planets' sizes unchanged, the planets would reflect around 4*10-7 of the Sun's light. Still tiny.
The only time you get anything that isn't tiny is in the case of a close binary. If another star the same size as the Sun orbited the Sun just one solar diameter away, it would intercept (and thus have the possibility of reflecting) around 6% of the sun's light.
This supports James K's conclusion pretty strongly.