  A search for strongly produced supersymmetric particles is conducted using
signatures involving multiple energetic jets and either two isolated leptons
($e$ or $\mu$) with the same electric charge or at least three isolated
leptons. The search also utilises $b$-tagged jets, missing transverse momentum
and other observables to extend its sensitivity. The analysis uses a data
sample of proton-proton collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS
detector at the Large Hadron Collider in 2015 corresponding to a total
integrated luminosity of 3.2 fb$^{-1}$. No significant excess over the Standard
Model expectation is observed. The results are interpreted in several
simplified supersymmetric models and extend the exclusion limits from previous
searches. In the context of exclusive production and simplified decay modes,
gluino masses are excluded at 95% confidence level up to 1.1-1.3 TeV for light
neutralinos (depending on the decay channel), and bottom squark masses are also
excluded up to 540 GeV. In the former scenarios, neutralino masses are also
excluded up to 550-850 GeV for gluino masses around 1 TeV.
