  De Haas-van Alphen oscillations are studied for Fermi surfaces illustrating
the Pippard's model, commonly observed in multiband organic metals. Field- and
temperature-dependent amplitude of the various Fourier components, linked to
frequency combinations arising from magnetic breakdown between different bands,
are considered. Emphasis is put on the Onsager phase factor of these
components. It is demonstrated that, in addition to the usual Maslov index,
field-dependent phase factors must be considered to precisely account for the
data at high magnetic field. We present compelling evidence of the existence of
such contributions for the organic metal theta-(BEDT-TTF)4CoBr4(C6H4Cl2).
