Generally, FFD have only two levels, high and low. but you can add a center point as third level. Or you can go through other methods like RSM, Taguchi
There is a 3-level design in Design Expert. Go to: New Design > Response Surface > Miscellaneous > 3-Level Factorial. I have attached a screengrab showing the same.
There are several ways to create 3-level designs in Design Expert. All of them have already been named in the answers above. But you have to ask yourself, why or for what purpose should such a design be created? This leads to at least two more questions. 1. Do I need a screening design for many factors about which I do not know much? Or do I want to find an optimal operating point for a process and have only a few important factors left in the design? 2. Do I want to create a 3-level design for cathegorial or continuous or for a mix of these factors? In case of continuous factors and the desire for process optimization, the answer is simple: RSM - estimating all quadratic terms is generally possible. A 2-level design with centerpoints only leads to an estimation of lack-of-fit and curvature. The effect strength of individual quadratic effects cannot be calculated. In the case of screening designs I would generally advise against 3-level designs, because they drive the number of runs up, fractional factorial designs are only possible to a limited extent (only via optimal designs) and this often leads to leaving important factors and their interactions out of the design to save runs. If cathegorial and continuous factors must be considered together in a design, then an optimal design from the chapter RSM is the right choice. This would then be a very specific application of a product and process optimization.