What would happen if I used the lice shampoo more than the recommended once a week?

Toxicity. Lice treatments are basically insecticides and if over-used will cause not only skin irritation but can cause neurologic toxicity (damage to the central nervous system). Children are especially susceptible to this.
Waste of product. There are some products with potential toxicity if used too often but the strength of these products makes it unlikely. I sometimes recommend retreating a week or so later to pick up any leftover bugs. It takes 10 days for the new louse to begin reproducing.