  This work provides a convenient and powerful means towards the engineering of
Floquet bands via Bloch oscillations, by adding a tilted linear potential to
periodically driven lattice systems. The added linear field not only restricts
the spreading of a time-evolving wavepacket but also, depending on the ratio
between the Bloch oscillation frequency and the modulation frequency of the
periodic driving, dramatically modifies the band profile and topology.
Specifically, we consider a driven Aubry-Andr\'e-Harper model as a working
example, in the presence of a linear field. Almost flat Floquet bands or
Floquet bands with large Chern numbers due to the interplay between the
periodic driving and Bloch oscillations can be obtained, with the band
structure and topology extensively tunable by adjusting the ratio of two
competing frequencies. To confirm our finding, we further execute the Thouless
pumping of one and two interacting bosons in such a lattice system and
establish its connection with the topological properties of single- and
two-particle Floquet bands.
