We propose a novel phone-case-shaped interface named TetraForce, which enables four types of force input consisting of two force directions (i.e., pressure force and shear force) and two force-applied surfaces (i.e., touch surface and back surface) in a single device. Force detection is achieved using the smartphone's built-in magnetometer (and supplementary accelerometer and gyro sensor) by estimating the displacement of a magnet attached to a 3-DoF passively movable panel at the back. We conducted a user study (N=12) to investigate the fundamental user performance by our interface and demonstrated that the input was detected as intended with a success rate of 97.4% on average for all four input types. We further conducted an ideation workshop with people who were involved in human-computer interaction (N=12) to explore possible applications of this interface, and we obtained 137 ideas for applications using individual input types and 51 possible scenarios using them in combination. Organizing these ideas reveals the advantages of each input type and suggests that our interface is useful for applications that require complex operations and that it can improve intuitiveness through elastic feedback.