  We construct a three-parameter deformation of the Hopf algebra $\LDIAG$. This
is the algebra that appears in an expansion in terms of Feynman-like diagrams
of the {\em product formula} in a simplified version of Quantum Field Theory.
This new algebra is a true Hopf deformation which reduces to $\LDIAG$ for some
parameter values and to the algebra of Matrix Quasi-Symmetric Functions
($\MQS$) for others, and thus relates $\LDIAG$ to other Hopf algebras of
contemporary physics. Moreover, there is an onto linear mapping preserving
products from our algebra to the algebra of Euler-Zagier sums.
