I propose that characters can be created with 24d6, taking the best 18 of those to group into 6 sets of 3d6 (one set for each ability score).
Below is why I think it isn't as broken a method as it might seem at first.
Currently, for d20 and D&D games, I have players roll 2 sets of ability scores using the normal rules in the PHB (i.e. roll 4d6 for each ability score and take the best 3 of those 4d6).
This gives players an average score of about 13 in each ability. Generally, the scores range from 8 to 16, with some higher and lower scores. (Less than 1.5 of the 6 scores are below 10.5 - the average roll of 3d6 - by this method.)
The new method averages out at about 12.65 in each ability score. Obviously, with the player making the selection of which die results to combine, some scores can be set higher - you are bound to get at least three 6s out of 24 dice.
However, grouping all your high values together to get some high-end scores leaves you with a collection of low results to make up your other ability scores.
Such a min-max set of scores is potentially more hampering than the 4d6, drop the lowest method - you will get more low scores if you simply arrange the dice in order of results.
(Around 2 of the 6 scores are below 10.5 if one simply arranges the dice from highest to lowest.)
Summary:
Though the 24d6 method looks better than the 4d6 method, the 4d6 method gives a higher average result.
24d6 generated characters maxing out scores will be balanced by having more low scores than their 4d6 counterparts.
The 24d6 method allows more flexibility and player control over ability scores.
