  (abridged) We present a spectroscopic analysis of five stellar streams (`A',
`B', `Cr', `Cp' and `D') as well as the extended star cluster, EC4, which lies
within streamC, all discovered in the halo of M31 from our CFHT/MegaCam survey.
These spectroscopic results were initially serendipitous, making use of our
existing observations from the DEep Imaging Multi-Object Spectrograph mounted
on the Keck II telescope, and thereby emphasizing the ubiquity of tidal streams
that account for ~70% of the M31 halo stars in the targeted fields. Subsequent
spectroscopy was then procured in streamCr/p and streamD to trace the velocity
gradient along the streams. For the cluster EC4, candidate member stars with
average [Fe/H]~-1.4 (Fe/H_spec=-1.6), are found at v_{hel}=-285 km/s suggesting
it could be related to streamCp. No similarly obvious cold kinematic candidate
is found for streamD, although candidates are proposed in both of two
spectroscopic pointings along the stream (both at -400 km/s). Spectroscopy near
the edge of streamB suggests a likely kinematic detection, while a candidate
kinematic detection of streamA is found (plausibly associated to M33 rather
than M31). The low dispersion of the streams in kinematics, physical thickness,
and metallicity makes it hard to reconcile with a scenario whereby these stream
structures as an ensemble are related to the giant southern stream. We conclude
that the M31 stellar halo is largely made up of multiple kinematically cold
streams.
