Due to a great number of composition-processing factors, it is very difficult to design high entropy amorphous alloys without performing manifold trial-and-error experimentations. To solve this problem, in this study we developed a machine learning-based approach, namely multilateral-based neural network, which is able to predict new high entropy amorphous compositions through estimating the highest glass forming ability and the critical casting thickness. In this approach, the entropy parameters were individually correlated to each input, which leads to the improvement of predictive model in evaluating the high entropy glassy alloys. As a case study, Ti20Zr20Hf20Be20Co20 high entropy metallic glass (MG) was considered and the effects of added elements such as Y, Ni, Cr and V and Cu on the glass formation and critical casting thickness were investigated. According to the results, it is determined that the Y addition acts as a microalloying process in the base composition, while other elements improve the configurational entropy and the total negative heat of mixing, which lead to the engineering of equi-atomic high entropy MGs.