  Recently it was shown that continuous Matrix Product States (cMPS) cannot
express the continuum limit state of any Matrix Product State (MPS), according
to a certain natural definition of the latter. The missing element is a
projector in the transfer matrix of the MPS. Here we provide a generalised
ansatz of cMPS that is capable of expressing the continuum limit of any MPS. It
consists of a sum of cMPS with different boundary conditions, each attached to
an ancilla state. This new ansatz can be interpreted as the concatenation of a
state which is at the closure of the set of cMPS together with a standard cMPS.
The former can be seen as a cMPS in the thermodynamic limit, or with matrices
of unbounded norm. We provide several examples and discuss the result.
