To use a different (alternate) approach to solving a problem when the standard approach doesn't work, an approach that is less complicated than improvising.
There was no bell at the hotel front desk, so we alternized by saying "ding, ding" until the clerk came out of the back room.
combination of alternative+fantastci=alternitastic
An alternative song (whether it be alternative rock/punk/indie/garage/etc) that is just absolutely fantastic in its own way (alternative way) can also be used to describe a band, singer, any thing relating to the genre alternative music.