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The fully matricial generalization in part I, of the difference quotientderivation on holomorphic functions, in which ${\mathbb C}$ is replaced by aBanach algebra $B$, is extended from the affine case to a Grassmanniancompletion. The infinitesimal bialgebra duality, the duality transformgeneralizing the Stieltjes transform and the spectral theory with non-commutingscalars all extend to this completion. The series expansions of fully matricialanalytic functions are characterized, providing a new way to generate fullymatricial functions.

Free Analysis Questions II: The Grassmannian Completion and The Series Expansions at the Origin