Can Single Source of Error (SSOE) models be implemented in MATLAB?

I would like to know whether or not it is possible to build "Single Source of Error" (SSOE) state-space models in MATLAB using the Econometrics Toolbox (or some other Toolbox).

The SSOE class of models are also sometimes called "linear innovations" state-space models. The distinguishing feature of SSOE models is that, unlike "Multiple Source of Error" (MSOE) models, the observation errors and state errors are allowed to be perfectly correlated.

The MATLAB documentation for the ssm class, states that:

$\epsilon_{t}$ and $u_{t}$ are uncorrelated ,

where $\epsilon_{t}$ and $u_{t}$ refer to the observation and state errors, respectively.

Does MATLAB allow the possibility to build state-space models were $\epsilon_{t}$ and $u_{t}$ are, in fact, perfectly correlated ?

Of course, this sort of model can be programmed from scratch, but I'm specifically asking if there are packaged tools, e.g. ssm class in the econometrics toolbox, that can be used to do it.

Many thanks.