Electroproduction form factors describing the γ * p → ∆ + (1232), ∆ + (1600) transitions are computed using a fully-dynamical diquark-quark approximation to the Poincaré-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the ∆(1600) is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the ∆(1232). Precise measurements of the γ * p → ∆ + (1232) transition already exist on 0 ≤ Q 2 8 GeV 2 and the calculated results compare favourably with the data outside the meson-cloud domain. The predictions for the γ * p → ∆ + (1600) magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to Q 2 ≈ 6m 2 p , enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the ∆-baryons. Interestingly, whilst the γ * p → ∆ + (1232) transition form factors are larger in magnitude than those for γ * p → ∆ + (1600) in some neighbourhood of the real photon point, this ordering is reversed on Q 2 2m 2 p , suggesting that the γ * p → ∆ + (1600) transition is more localised in configuration space.