  The strong equivalence principle is a cornerstone of general relativity,
tested with exquisite accuracy in the Solar system. However, tests in the
strong-field regime require a compact object. Currently, PSR J0337+1715 is the
unique millisecond pulsar found in a triple stellar system, orbiting two white
dwarfs within an area comparable to the orbit of the Earth. This configuration
offers the opportunity for a dramatic improvement over previous tests, provided
that accurate and regular timing of the pulsar can be achieved. This also
requires the development of a new timing model solving numerically the
relativistic three-body problem with great accuracy. We report on the analysis
of the high-quality dataset gathered on PSR J0337+1715 by the Nan{\c c}ay
radiotelescope over the past 8 years. In particular, I will show how we could
obtain the most stringent limit to-date on a potential violation of the strong
equivalent principle in the strong field regime. I will also introduce
preliminary resuts showing that the presence of a small planet in the system
may explain a tiny residual signal so far unaccounted for, which if confirmed
would make this system exceptionally rich.
