  The Gurari\u{\i} space is the unique separable Banach space $\mathbb{G}$
which is of almost universal disposition for finite-dimensional Banach spaces,
which means that for every $\varepsilon>0$, for all finite-dimensional normed
spaces $E \subseteq F$, for every isometric embedding
${e}\colon{E}\to{\mathbb{G}}$ there exists an $\varepsilon$-isometric embedding
${f}\colon{F}\to{\mathbb{G}}$ such that $f \restriction E = e$.
  We show that $\mathbb{G}^{\mathbb{N}}$ with a special sequence of semi-norms
is of almost universal disposition for finite-dimensional graded Fr\'echet
spaces. The construction relies heavily on the universal operator on the
Gurari\u{\i} space, recently constructed by Garbuli\'nska-Wegrzyn and the third
author.
  This yields in particular that $\mathbb{G}^{\mathbb{N}}$ is universal in the
class of all separable Fr\'echet spaces.
