  The direct detection of gravitational waves provides the opportunity to
measure fundamental aspects of gravity which have never been directly probed
before, including the polarization of gravitational waves. In the context of
searches for continuous waves from known pulsars, we present novel methods to
detect signals of any polarization content, measure the modes present and place
upper-limits on the amplitude of non-tensorial components. This will allow us
to obtain new model-independent, dynamical constraints on deviations from
general relativity. We test this framework on multiple potential sources using
simulated data from three advanced-era detectors at design sensitivity. We find
that signals of any polarization will become detectable and distinguishable for
characteristic strains $h\gtrsim 3\times10^{-27} \sqrt{1~{\rm yr}/T}$, for an
observation time $T$. We also find that our ability to detect non-tensorial
components depends only on the power present in those modes, irrespective of
the strength of the tensorial strain.
