  We investigate the landscape of generalized geometries that can be derived
from Monge-Amp\`ere structures. Instead of following the approaches of Banos,
Roubtsov, Kosmann-Schwarzbach, and others, we take a new path inspired by the
results of Hu, Moraru, and Svoboda. We construct a large family of new
generalized almost geometries derived from non-degenerate 2D symplectic
Monge-Amp\`ere structures and other related geometric objects, such as complex
structures. We demonstrate that, under certain assumptions, non-degenerate
Monge-Amp\`ere structures give rise to quadric surfaces of generalized almost
geometries. Additionally, we discuss the link between Monge-Amp\`ere structures
and Monge-Amp\`ere equations within this framework.
