Which pattern of inheritance results from individual organisms having many different genes working at the same time to control a single trait?

The answer is polygenic inheritance.

Many physical characters (traits) depend on many different factors, each of which is determined by different genes. This is called polygenic inheritance.
For example, the color of the skin in humans. The color of the skin results from the interactions of several factors determined by different pairs of genes:

-Certain genes could affect the metabolism of skin melanocytes.
-Other genes can determine the distribution of melanin in the thickness of the skin.
-Some genes could determine the relative amounts of each of the two possible types of melanin.
-Others may affect the production of certain hormones involved in the activity of melanocytes.