A type of "stock swap" option exercise in which you pay cash to exercise the first option, and then a small number of previously owned shares is surrendered to the company to pay a portion of the exercise price, for which a slightly larger number of option shares may be purchased. These are then immediately swapped back to the company to pay additional amounts of the exercise price, and so on until the remainder of the options have been exercised. In the end you have a number of shares equal in value to the option "spread" (similar to a net exercise
or stock-settled SARs).
With the advent of broker-assisted "cashless exercise/same-day sale" programs, pyramiding has fallen out of favor. However, FAS 123(R) (now called ASC Topic 718) no longer requires shares to be held for six months before they are mature, so pyramid exercises may regain popularity for NQSOs. For details about stock swaps, see a related FAQ.