A search is presented for an extended Higgs sector with two new particles, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>X</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ϕ</c:mi></c:math>, in the process <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mi>X</e:mi><e:mo stretchy="false">→</e:mo><e:mi>ϕ</e:mi><e:mi>ϕ</e:mi><e:mo stretchy="false">→</e:mo><e:mo stretchy="false">(</e:mo><e:mi>γ</e:mi><e:mi>γ</e:mi><e:mo stretchy="false">)</e:mo><e:mo stretchy="false">(</e:mo><e:mi>γ</e:mi><e:mi>γ</e:mi><e:mo stretchy="false">)</e:mo></e:mrow></e:math>. Novel neural networks classify events with diphotons that are merged and determine the diphoton masses. The search uses LHC proton-proton collision data at <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msqrt><m:mrow><m:mi>s</m:mi></m:mrow></m:msqrt><m:mo>=</m:mo><m:mn>13</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>TeV</m:mi></m:mrow></m:math> collected with the CMS detector, corresponding to an integrated luminosity of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>138</o:mn><o:mtext> </o:mtext><o:mtext> </o:mtext><o:msup><o:mi>fb</o:mi><o:mrow><o:mo>−</o:mo><o:mn>1</o:mn></o:mrow></o:msup></o:math>. No evidence of such resonances is seen. Upper limits are set on the production cross section for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>m</q:mi><q:mi>X</q:mi></q:msub></q:math> between 300 and 3000 GeV and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>m</s:mi><s:mi>ϕ</s:mi></s:msub><s:mo>/</s:mo><s:msub><s:mi>m</s:mi><s:mi>X</s:mi></s:msub></s:math> between 0.5% and 2.5%, representing the most sensitive search in this channel. © 2025 CERN, for the CMS Collaboration 2025 CERN