A search is presented for an extended Higgs sector with two new particles, X and $\phi$, in the process X $\to$ $\phi\phi$ $\to$ $(\gamma\gamma)(\gamma\gamma)$. Novel neural networks classify events with diphotons that are merged and determine the diphoton masses. The search uses LHC proton-proton collision data at $\sqrt{s}$ = 13 TeV collected with the CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$. No evidence of such resonances is seen. Upper limits are set on the production cross section versus the resonance masses, representing the most sensitive search in this channel.