Really you think that is possible, the US had to practically grovel to make the public understand that more troops were needed and to make the Europeans commit more.
The more troops you will commit the more the death toll will rise and more your presence will be sledge hammered by the media.
Not to mention that the Afghans despise you, they despise all foreign troops on their soil, the amount of troops needed to take complete control of the mountains and the country side will exceed 500000(my rough estimation), this no. of foreign soldiers will be seen as threats by the Afghans and the extremists will use this to recruit more troops. Most Taliban recruits believe that they are fighting foreign invaders, most don't believe the terrorist views, they believe they are freedom fighters. Afghans will always oppose Foreign troops, they are too proud.
Also you forget that Afghans hate each other, their is too much racial hate there, the US wants to make Pashtuns, Hazaras, Tajiks live together, something they do not want to, for generations they have believed that Afghanistan belongs to their respective race and for generations they have hated each other, you cannot remove so much bad blood easily. It will take decades worth of teaching children that thier for fathers were wrong and that all races should respect each other and live together peacefully. You are trying to help a people who need help but do not want it, they oppose it. The only way you can make Afghanistan stable would be to break into separate states each state for each race and monitor the borders to prevent war.