We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system $i\partial ₜu+\Delta u=\lambda ₁\left|u\right|⁴u+\lambda ₂b₁u{v}_{x₁}$, $-\Delta v=b₂{\left(\right|u\left|²\right)}_{x₁}$. Under certain conditions on λ₁ and λ₂, we provide a complete picture of the local and global well-posedness, scattering and blow-up of the solutions in the energy space. Methods used in the paper are based upon the perturbation theory from [Tao et al., Comm. Partial Differential Equations 32 (2007), 1281-1343] and the convexity method from [Glassey, J. Math. Phys. 18 (1977), 1794-1797].