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Let P be a closed convex cone in 
$\mathbb{R}^d$ which is assumed to be spanning 
$\mathbb{R}^d$ and contains no line. In this article, we consider a family of CAR flows over P and study the decomposability of the associated product systems. We establish a necessary and sufficient condition for CAR flow to be decomposable. As a consequence, we show that there are uncountable many CAR flows which are cocycle conjugate to the corresponding CCR flows.
In this paper, we construct uncountably many examples of multiparameter CCR flows, which are not pullbacks of $1$
-parameter CCR flows, with any given index. Moreover, the constructed CCR flows are type I in the sense that the associated product system is the smallest subsystem containing its units.
