We investigate rogue wave (RW) clusters composed of Kuznetsov–Ma solitons (KMSs) from the nonlinear Schrödinger equation (NLSE) with Kerr nonlinearity. We present three classes of exact higher-order solutions on uniform background that are calculated using the Darboux transformation (DT) scheme with precisely chosen parameters. The first solution class is characterized by strong-intensity narrow peaks that are periodic along the evolution axis when the eigenvalues in the DT scheme generate KMSs with commensurate frequencies. The second solution class has a form of elliptical rogue wave clusters and it is derived from the previous solution class when the first m evolution shifts in the nth-order DT scheme are equal and nonzero. We show that the high-intensity peaks built on KMSs of order n − 2m periodically appear along the evolution axis. This central rogue wave is enclosed by m ellipses consisting of a certain number of the first-order KMSs determined by the ellipse index and the solution order. The third class of KMS clusters is calculated when purely imaginary DT eigenvalues tend to some preset offset value higher than one while keeping the evolution shifts unchanged. We show that the central rogue wave at the plane origin retains its n − 2m order. The n tails composed of the first-order KMSs are formed above and below the central maximum. For even n, more complicated patterns are generated, with m loops above and m − 1 loops below the central RW.