  The Collins effect describes the modulation of the hadron production by a
transversely polarized quark with the sine of the polar angle, $\varphi$,
between the produced hadron's transverse momentum and the quark spin. We employ
a quark-jet model to describe multiple hadron emissions by such a quark, taking
the Collins effect into account. The resulting hadron distributions exhibit
modulation up to fourth order in $\sin(\varphi)$ when only two hadron emissions
are allowed, rising with any further increase in the number of emitted hadrons.
These new effects are a direct consequence of the quark-jet mechanism for quark
hadronization, which do not depend on the details of the model used for
elementary hadron emission. The size and the sign of the higher order terms are
directly connected with the probabilities of quark spin flip in the elementary
emission process, with opposing sign favored and unfavored Collins functions
only being generated if quark spin flip is preferential. Experimental studies
of these effects should therefore provide a critical test of the quark
hadronization mechanism, which in turn will lead to a deeper understanding of
the transverse spin structure of hadrons.
