The benefits and theory of front-loading are well-known. In essence, front-loading peaks the blood levels in the first weeks of the cycle as opposed to much later. For example, taking 1000mg of test e the first week of the 500mg per week cycle will achieve approximately what normally takes 7 weeks to achieve, with respect to blood levels.
Under this theory, would doubling the dosage in, let's say, the third-week, serve the same purpose, albeit later? For example, after taking 250mg of test e 2x a week for two weeks, would taking 500 2x during the third week (mid-load), get your blood levels to full peak?
In practice, I don't see any advantage to this but might be used by someone who failed to front-load immediately and desires to speed things along.