You can - if your base is a slat type, fixed or flexi, or a solid base of some type. However if you have a sprung type of base it acts like a large shock absorber, taking a lot of the nightly wear and tear. So it is an important contributor to the comfort and support of a bed. A new mattress can only be as good as its base allows as the mattress will follow any lumps or hollows. Replace as a set, the two are designed to work together.