  Context: It appears that most (if not all) massive stars are born in multiple
systems. At the same time, the most massive binaries are hard to find due to
their low numbers throughout the Galaxy and the implied large distances and
extinctions. AIMS: We want to study: [a] LS III +46 11, identified in this
paper as a very massive binary; [b] another nearby massive system, LS III +46
12; and [c] the surrounding stellar cluster, Berkeley 90. Methods: Most of the
data used in this paper are multi-epoch high-S/N optical spectra though we also
use Lucky Imaging and archival photometry. The spectra are reduced with devoted
pipelines and processed with our own software, such as a spectroscopic-orbit
code, CHORIZOS, and MGB. Results: LS III +46 11 is identified as a new
very-early-O-type spectroscopic binary [O3.5 If* + O3.5 If*] and LS III +46 12
as another early O-type system [O4.5 V((f))]. We measure a 97.2-day period for
LS III +46 12 and derive minimum masses of 38.80$\pm$0.83 M_Sol and
35.60$\pm$0.77 M_Sol for its two stars. We measure the extinction to both
stars, estimate the distance, search for optical companions, and study the
surrounding cluster. In doing so, a variable extinction is found as well as
discrepant results for the distance. We discuss possible explanations and
suggest that LS III +46 12 may be a hidden binary system, where the companion
is currently undetected.
