Aims. Near-IR photometry of dwarf irregular galaxies (dIs) has been acquired to expand the sample of objects suitable for investigating the fundamental plane (FP) discovered previously by us. Data for blue compact dwarfs (BCDs), dwarf ellipticals (dEs), and dwarf spheroidal galaxies (dSphs) are amalgamated to evaluate how closely these classes of galaxies are related to dIs. Methods. Surface brightness profiles for dIs are modeled using a hyperbolic secant function (sech), which has been shown to sample the old galaxy component observed in the NIR (Ks). Also, profiles for BCDs are modeled using a sech function, but to this is added a Gaussian burst. Kinematics for dIs and BCDs are constrained by the width W20 of integrated HI line profiles, and motions within dEs and dSphs are judged from stellar velocity dispersions. Results. The existence of a FP for dIs is confirmed. Omitting extreme deviants, the scatter of dIs about the plane is 0.43 mag, somewhat higher than expected from observational errors alone. Corrections of line widths for tilt do not reduce the residuals, so motions must be predominantly random. Corrections of surface brightnesses for tilt have no effect either. BCDs and dEs lie precisely on the FP defined by dIs, suggesting strong underlying connections among dIs, BCDs, and dEs.