  The purpose of this paper is to study the Sasakian geometry on odd
dimensional sphere bundles over a smooth projective algebraic variety $N$ with
the ultimate, but probably unachievable goal of understanding the existence and
non-existence of extremal and constant scalar curvature Sasaki metrics. We
apply the fiber join construction of Yamazaki \cite{Yam99} for K-contact
manifolds to the Sasaki case. This construction depends on the choice of $d+1$
integral K\"ahler classes $[\omega_j]$ on $N$ that are not necessarily colinear
in the K\"ahler cone. We show that the colinear case is equivalent to a
subclass of a different join construction orginally described in
\cite{BG00a,BGO06}, applied to the spherical case by the authors in
\cite{BoTo13,BoTo14a} when $d=1$, and known as cone decomposable \cite{BHLT16}.
The non-colinear case gives rise to infinite families of new inequivalent cone
indecomposable Sasaki contact CR on certain sphere bundles. We prove that the
Sasaki cone for some of these structures contains an open set of extremal
Sasaki metrics and, for certain specialized cases, the regular ray within this
cone is shown to have constant scalar curvature. We also compute the cohomology
groups of all such sphere bundles over a product of Riemann surfaces.
