Can an organism will itself to adapt to a new environment so it can increase its fitness?

Yes, an organism does adapts itself to the new environment in order to increase its fitness. Each organism has its unique ecosystem in which it lives. This is where all of its necessary needs of water, food and reproduction are met.

In order to survive, an organism has to adapt to its habitat which helps to compete and survive in that ecosystem.This modification or adaptation helps the organism to survive and be fit for its habitat.