III-V semiconductors, such as Aluminium Gallium Arsenide (AlGaAs), are known for their high refractive index and strong non-resonant second-order optical nonlinearity making them useful for building active nonlinear photonic devices. AlGaAs-based nanophotonic structures supporting anapole resonances can significantly boost the internal electric fields resulting in enhanced nonlinear optical response. However, low-quality factors of these anapolar resonances can result in poor conversion efficiency for the nonlinear optical process. Here we report enhanced sum frequency generation (SFG) from vertically stacked three-disk AlGaAs-based nanoresonators supporting anapole type resonance that exhibit an order of magnitude increase in field enhancement compared to a single-disk resonator system at the SFG wavelength. The vertically stacked resonators consist of three individual AlGaAs layers separated vertically by an under-cut Gallium Arsenide (GaAs) stem. Finite difference time domain (FDTD) simulations of the scattering cross sections were performed to optimize the dimensions of AlGaAs resonator. The optimal structure consists of three vertically stacked AlGaAs nanodisks (550 nm diameter, 50 nm height) separated by a 100 nm GaAs stem. This design ensures anapole type resonance overlap at SFG wavelength (600-670 nm). Multi-spectral SFG images were acquired by varying the input signal wavelength in the range of 1400-1800 nm, keeping the pump wavelength fixed at 1040 nm. The experimental results show a maximum SFG enhancement of approximately 50-times near the resonance wavelength of 645 nm in comparison to unpatterned multilayer samples. Optical nanostructures based on stacked AlGaAs resonators provide a very exciting platform to tailor the light-matter interactions for linear and non-linear optical applications.