Change to a *GT? That is the discounted rate...and generally no. IGT offers typically (not always but usually) come out after the PIF date. And they always require a "new" booking, paid in full at the time of booking. What you might be able to do is cancel the existing reservation and book a new IGT. But if it's after PIF be sure to calculate the penalty to determine if it's worth it.
If you mean a regular GTY (such as 4A GTY) that isn't a discounted rate and will almost always be higher than an earlier booking for the same room category.