  Higgs boson compositeness is a phenomenologically viable scenario addressing
the hierarchy problem. In minimal models, the Higgs boson is the only degree of
freedom of the strong sector below the strong interaction scale. We present
here the simplest extension of such a framework with an additional composite
spin-zero singlet. To this end, we adopt an effective field theory approach and
develop a set of rules to estimate the size of the various operator
coefficients, relating them to the parameters of the strong sector and its
structural features. As a result, we obtain the patterns of new interactions
affecting both the new singlet and the Higgs boson's physics. We identify the
characteristics of the singlet field which cause its effects on Higgs physics
to dominate over the ones inherited from the composite nature of the Higgs
boson. Our effective field theory construction is supported by comparisons with
explicit UV models.
