With the rapidly growing interest in the use of mesenchymal stromal cells (MSCs) for cell therapy and regenerative medicine applications, either alone as an injected suspension, or dispersed within injectable hydrogel delivery systems, greater understanding of the structure-function-property characteristics of suspensions of adhesion-dependent mesenchymal cells is required. In this paper, we present the results of an experimental study into the flow behavior of concentrated suspensions of living cells of mesenchymal origin (fibroblasts) over a wide range of cell concentrations, with and without the addition of hyaluronic acid (HA), a commonly utilized biomolecule in injectable hydrogel formulations. We characterize the change in the shear viscosity as a function of shear stress and shear rate for cell volume fractions varying from 20 to 60%. We show that high volume fraction suspensions of living mesenchymal cells, known to be capable of homotypic interactions, exhibit highly complex but reproducible rheological footprints, including yield stress, shear thinning and shear-induced fracture behaviors. We show that with the addition of HA, we can significantly modify and tailor the rheology of these cell suspensions at all volume fractions. Using FACS and confocal imaging, we show that the observed effect of HA addition is due to a significantly modulation in the formation of cellular aggregates in these suspensions, and thus the resultant volume spanning network. Considering the aggregates as fractal structures, we show that by taking into account the changes in volume fractions with shear, we are able to plot a master curve for the range of conditions investigated and extract from it the average adhesion force between individual cells, across a population of millions of cells. The outcomes of this study not only provide new insight into the complexity of the flow behaviors of concentrated, adhesive mesenchymal cell suspensions, and their sensitivity to associative biomacromolecule addition, but also a novel, rapid method by which to measure the average adhesion force between individual cells, and the impacts of biomacromolecules on this important parameter.