  Context. HD 95086 is a young nearby Solar System analog hosting a giant
exoplanet orbiting at 57 au from the star between an inner and outer debris
belt. The existence of additional planets has been suggested as the mechanism
that maintains the broad cavity between the two belts.
  Aims. We present a dedicated monitoring of HD 95086 with the VLT/SPHERE
instrument to refine the orbital and atmospheric properties of HD 95086 b, and
to search for additional planets in this system.
  Methods. SPHERE observations, spread over ten epochs from 2015 to 2019 and
including five new datasets, were used. Combined with archival observations,
from VLT/NaCo (2012-2013) and Gemini/GPI (2013-2016), the extended set of
astrometric measurements allowed us to refine the orbital properties of HD
95086 b. We also investigated the spectral properties and the presence of a
circumplanetary disk around HD 95086 b by using the special fitting tool
exploring the diversity of several atmospheric models. In addition, we improved
our detection limits in order to search for a putative planet c via the
K-Stacker algorithm.
  Results. We extracted for the first time the JH low-resolution spectrum of HD
95086 b by stacking the six best epochs, and confirm its very red spectral
energy distribution. Combined with additional datasets from GPI and NaCo, our
analysis indicates that this very red color can be explained by the presence of
a circumplanetary disk around planet b, with a range of high-temperature
solutions (1400-1600 K) and significant extinction (Av > 10 mag), or by a
super-solar metallicity atmosphere with lower temperatures (800-1300 K), and
small to medium amount of extinction (Av < 10 mag). We do not find any robust
candidates for planet c, but give updated constraints on its potential mass and
location.
