Transform margins are first-order tectonic features that accommodate oceanic spreading.Uncertainties remain about their evolution, genetic relationship to oceanic spreading, and general structural character. When the relative motion of the plates changes during the margin evolution, further structural complexity is added. This work investigates the evolution of transform margins and associated rift-transform intersections, using an analogue modeling approach that simulates changing plate motions. We investigate the effects of different crustal rheologies by using either (a) a two-layer brittle-ductile configuration to simulate upper and lower continental crust, or (b) a single layer brittle configuration to simulate oceanic crust. The modeled rifting is initially orthogonal, followed by an imposed plate vector change of 7°that results in oblique rifting and plate overlap (transpression) or underlap (transtension) along each transform margin. This oblique deformation reactivates and overprints earlier orthogonal structures and is representative of natural examples. We find that (a) a transtensional shift in the plate direction produces a large strike-slip principal displacement zone, accompanied by en-echelon oblique-normal faults that accommodate the horizontal displacement until the new plate motion vector is stabilized, while (b) a transpressional shift produces compressional structures such as thrust fronts in a triangular zone in the area of overlap. These observations are in good agreement with natural examples from the Gulf of California (transtensional) and Tanzania Coastal Basin (transpressional) shear margins and illustrate that when these deformation patterns are present, a component of plate vector change should be considered in the evolution of transform margins.Plain Language Summary Tectonic plate boundaries on our planet are categorized by their relative motion with respect to each other. The three main categories are those moving away, toward, and parallel to one another. We study the processes occurring when two tectonic plates moving parallel begin to rotate and move away or toward each other. Currently, this is occurring in the Gulf of California, and in the past, it occurred in areas such as the Southern Atlantic, creating the segmented pattern along its midocean ridge. To study these tectonic plate boundaries, we use sandbox modeling. We make miniature models of the Earth's crust with silicone putty and sand and recreate the same movements that tectonic plates go through. This allows us to understand the structures created in such environments better. The pattern and the height or depth of these structures are related to how fast the plates move. This work can help recognize areas where similar deformation has occurred in the past, which is important for hydrocarbon exploration. It can also assist with geothermal energy exploration, as areas where plates move parallel and away from each other present good opportunities for hotter temperatures in the subsurface.