  The BL Lac PG 1553+113 has been continuously monitored in gamma rays with
Fermi-LAT for over 9 years. Its updated light curve now includes 5 iterations
of a main pattern comprising a high peak and a longer trough, with a period P
\sim 2.2 yr. Our analysis of 2015-2017 data confirms the occurrence in January
2017 of a new peak fitting in the previous trend. In addition, we identify
secondary peaks ("twin peaks") that occur in closely symmetric pairs on both
sides of most main peaks, including the last one; their occurrence is supported
by correlated X-ray outbursts. We stress that the above features strongly point
to binary dynamics in a system of two black holes (BHs) of some 10^8 and 10^7
M_sun. At periastron the smaller BH periodically stresses the jet j_1 launched
by the heavier companion, and triggers MHD-kinetic tearing instabilities. These
lead to magnetic reconnections and to acceleration of electrons that produce
synchrotron emission from the optical to X-ray bands, and inverse Compton
scattering into the GeV range. For the origin of the twin peaks we discuss two
possibilities: a single-jet model, based on added instabilities induced in j_1
by the smaller companion BH on its inner orbital arc; and a two-jet model with
the smaller BH supporting its own, precessing jet j_2 that contributes lower,
specific GeV emissions. Such behaviors combining time stability with amplitude
variations betray plasma instabilities driven in either jet by binary dynamics,
and can provide a double signature of the long-sought supermassive BH binaries.
