We study the non-monotonic Keplerian velocity profiles related to locally nonrotating frames (LNRF) in the field of near-extreme braneworld Kerr black holes and naked singularities in which the non-local gravitational effects of the bulk are representedby a braneworld tidal charge b and the 4D geometry of the spacetime structure is governed by the Kerr?Newman geometry. We show that positive tidal charge has a tendency to restrict the values of the black hole dimensionless spin a admitting existence ofthe non-monotonic Keplerian LNRF-velocity profiles; the non-monotonic profiles exist in the black hole spacetimes with tidal charge smaller than b D 0:41005 (and spin larger than a D 0:76808). With decreasing value of the tidal charge (which need not beonly positive), both the region of spin allowing the non-monotonicity in the LNRF-velocity profile around braneworld Kerr black hole and the velocity difference in the minimum-maximum parts of the velocity profile increase implying growin