We demonstrate a neural network capable of designing on-demand multiple symmetry-protected bound states in the continuum (BICs) in freeform structures with predefined symmetry. The latent representation of the freeform structures allows the tuning of the geometry in a differentiable, continuous way. We show the rich band inversion and accidental degeneracy in these freeform structures by interacting with the latent representation directly. Moreover, a high design accuracy is demonstrated for arbitrary control of multiple BIC frequencies by using a photonic property readout network to interpret the latent representation.