  The formation process of high-mass stars (>8M$_\odot$) is poorly constrained,
particularly, the effects of clump fragmentation creating multiple systems and
the mechanism of mass accretion onto the cores. We study the fragmentation of
dense gas clumps, and trace the circumstellar rotation and outflows by
analyzing observations of the high-mass (~500M$_\odot$) star-forming region
IRAS 23033+5951. Using the Northern Extended Millimeter Array (NOEMA) in three
configurations and the IRAM 30-m single-dish telescope at 220GHz, we probe the
gas and dust emission at an angular resolution of ~0.45arcsec, corresponding to
1900au. In the mm continuum emission, we identify a protostellar cluster with
at least four mm-sources, where three of them show a significantly higher peak
intensity well above a signal-to-noise ratio of 100. Hierarchical fragmentation
from large to small spatial scales is discussed. Two fragments are embedded in
rotating structures and drive molecular outflows, traced by $^{13}$CO (2-1)
emission. The velocity profiles across two of the cores are similar to
Keplerian but are missing the highest velocity components close to the center
of rotation, which is a common phenomena from observations like these, and
other rotation scenarios are not excluded entirely. Position-velocity diagrams
suggest protostellar masses of ~6 and 19M$_\sun$. Rotational temperatures from
fitting CH$_3$CN ($12_K-11_K$) spectra are used for estimating the gas
temperature and by that the disk stability against gravitational fragmentation,
utilizing Toomre's $Q$ parameter. [We] identify only one candidate disk to be
unstable against gravitational instability caused by axisymmetric
perturbations. The dominant sources cover different evolutionary stages within
the same maternal gas clump. The appearance of rotation and outflows of the
cores are similar to those found in low-mass star-forming regions.
