Hiding a Higgs width enhancement from off-shellgg(→h*)→ZZmeasurements

Measurements of the off-shell Higgs boson production cross section in $gg(\ensuremath{\rightarrow}{h}^{*})\ensuremath{\rightarrow}ZZ$ have recently been used by the CMS and ATLAS collaborations to indirectly constrain the total width of the Higgs boson. I point out that the interpretation of these measurements as a Higgs width constraint can be invalidated if additional neutral Higgs boson(s) are present with masses below about 350 GeV.