Abstract: The LHCb Collaboration has recently observed four J/psi phi structures called X(4140), X(4274), X(4500), and X(4700) in the B+ -> J/psi phi K+ decays. We study them herein using a nonrelativistic constituent quark model in which the degrees of freedom are quark-antiquark and meson-meson components. The X(4140) resonance appears as a cusp in the J/psi phi channel due to the near coincidence of the D-s(+/-) D-s(*+/-) and J/psi phi mass thresholds. The remaining three [X(4274), X(4500), and X(4700)] appear as conventional charmonium states with quantum numbers 3(3)P(1), 4(3)P(0), and 5(3)P(0), respectively, and their masses and widths are slightly modified due to their coupling with the corresponding closest meson-meson thresholds. A particular feature of our quark model is a lattice-based screened linear confining interaction that has been constrained in the light-quark sector and usually produces higher excited heavy-quark states with lower masses than standard quark model predictions.