Is there evidence of multiple poles (higher order than dipole) in earth's magnetic field?
It's common for dynamo models to predict a large reduction in the dipole field during a reversal. Proving it in the paleomagnetic record is another matter entirely. To characterize the geometry of the magnetic field, you need several simultaneous measurements, preferably with a good spatial distribution. Instead what you get are relatively infrequent, asynchronous measurements. See this article by Fabio Florindo for more details. For what it's worth, though, a model by Olson et al. (2011) with multipolar fields during the transition predicts some observations that are consistent with the Matayama-Brunhes transition, including reductions in the intensity of the field and variations in the virtual geomagnetic pole path (VGP) from one site to another (see page 124 of this book for a definition of a VGP).