This paper is dedicated to the design of fully steerable linear differential microphone arrays (LDMAs). We analyze the steerable ideal spatial responses and explain why conventional LDMAs consisting of only omnidirectional microphones have limited steering ability. In order to circumvent this limitation, we suggest to use both omnidirectional and bidirectional (with a dipole shaped directivity pattern) microphones. We discuss the minimum numbers of omnidirectional and bidirectional sensors required for achieving steerable spatial responses and present a method to design fully steerable differential beamformers with LDMAs through the Jacobi-Anger series expansion. Simulations validate the presented technique and the steering flexibility of the designed LDMAs.