  We consider stationary axially symmetric black holes with the background
scalar field and test particles that can interact with this field directly.
Then, particle collision near a black hole can lead to the unbounded energy $%
E_{c.m.}$ in the centre of mass frame (contrary to some recent claims in
literature). This happens always if one of particles is neutral whereas another
one has nonzero scalar charge. Kinematically, two cases occur here. (i) A
neutral particle approaches the horizon with the speed of light while the
velocity of the charged one remains separated from it (this is direct analogue
of the situation with collision of geodesic particles.). (ii) Both particles
approach the horizon with the speed almost equal to that of light but with
different rates. As a result, in both cases the relative velocity also
approaches the speed of light, so that $E_{c.m.}$ $\ $becomes unbounded. We
consider also a case when the metric coefficient $g_{\phi \phi }\rightarrow 0$
near a black hole. Then, overlap between the geometric factor and the presence
of the scalar field opens additional scenarios in which unbounded energy
$E_{c.m.}$ is possible as well. We give a full list of possible scenarios of
high-energy collisions for the situations considered.
