Medical image registration can be challenging, in that optimal solutions depend on the application domain (unimodal, multimodal, intra-subject and inter-subject), anatomical sites (e.g., brain, spinal cord (SC) and lungs), dimensionality of the data (2D, 3D and 4D), deformation constraints (rigid, affine and nonlinear) and computational time. Solutions that could accommodate a large variety of applications while producing satisfactory results are needed. SynthMorph was recently introduced as an unsupervised deep learning–based registration method. A particularly interesting feature is that training is performed on synthetic data so that registration becomes agnostic to image contrast and anatomy. However, SynthMorph is particularly sensitive to the initial closeness of the images. In this work, we extend the SynthMorph method by developing a cascaded pipeline of two models that can accommodate large and fine deformations, respectively. We also validate this pipeline for the registration of intra-subject multimodal and inter-subject uni/multimodal MRI data of the SC. This task is known to be particularly difficult due to the vicinity of multiple tissue types whose morphometrics can vary substantially across subjects and contrasts. Evaluation of the method was conducted on a publicly available dataset (spine-generic, 267 subjects) and was compared with a state-of-the-art benchmark: Spinal Cord Toolbox and Advanced Normalization Tools. Results demonstrate better registration accuracy compared with the benchmark and about 24–30 times faster on CPUs depending on the image size. This proposed pipeline provides an easy-to-use, accurate and fast solution for multimodal 3D registration. The code and trained models are freely available at https://github.com/ivadomed/multimodal-registration.