  A search for strongly produced supersymmetric particles using signatures
involving multiple energetic jets and either two isolated same-sign leptons
($e$ or $\mu$), or at least three isolated leptons, is presented. The analysis
relies on the identification of $b$-jets and high missing transverse momentum
to achieve good sensitivity. A data sample of proton-proton collisions at
$\sqrt{s}= 13$ TeV recorded with the ATLAS detector at the Large Hadron
Collider in 2015 and 2016, corresponding to a total integrated luminosity of
36.1 fb$^{-1}$, is used for the search. No significant excess over the Standard
Model prediction is observed. The results are interpreted in several simplified
supersymmetric models featuring $R$-parity conservation or $R$-parity
violation, extending the exclusion limits from previous searches. In models
considering gluino pair production, gluino masses are excluded up to 1.87 TeV
at 95% confidence level. When bottom squarks are pair-produced and decay to a
chargino and a top quark, models with bottom squark masses below 700 GeV and
light neutralinos are excluded at 95% confidence level. In addition,
model-independent limits are set on a possible contribution of new phenomena to
the signal region yields.
