Multi-photon absorption (MPA) and free-carrier (FC) effects, usually considered to be detrimental to microcomb generation by introducing strong nonlinear loss, also offer opportunities to overwhelm the thermal-optic effect by modifying the refractive index. Here, we derive the theoretical expression of solitons expanded with MPA and FC effects, accompanied by numerical simulations to reveal the dynamics and mechanism for capturing steady mid-infrared solitons in both Si and Ge microcavities. It is found that with increased FC lifetime, the intensity-dependent MPA underlies non-monotonous variation of nonlinear detuning which enables soliton generation. More interestingly, proper control on the FC lifetime admits bidirectional switching of soliton states (i.e., both decreasing and increasing the number of solitons) as well as self-starting solitons, yielding different technique routes toward microcavity solitons. This research could contribute to a better understanding of nonlinear behaviors influenced by FC effects and find practical applications by releasing the demand on precise control of laser sources, which is especially meaningful for the mid-infrared region. © 2021 Author(s).