At the cellular level, plant growth results from the competition between the so-called turgor pressure and mechanical resistance from the cell walls. The turgor pressure itself results from a difference of osmotic pressure between the interior and the exterior of the cell: the plasmic membrane is semi-permeable, so that a higher solute (sugars, ions) concentration inside the cell leads to a water flux towards the cell and to a pressure rise; if the pressure exceeds a given threshold, the cell walls extend and the cell grows. Recently, different models of plant growth have attempted to incorporate mechanics of cell walls in tissue development [Boudon et al. 2015], but all of them make the assumption that turgor pressure is constant with time. In this work, we go one step further and include a model of the regulation of turgor pressure in a multicellular framework. The cell wall material is modeled as a continuous visco-elasto-plastic material characterized by an elastic modulus, a yield deformation, and a rate of synthesis of matter as in [Boudon et al. 2015]. Flows between cells occur through their membranes according to non-equilibrium thermodynamics, as a result from a difference in turgor and osmotic pressures. The value of pressure is not prescribed but emerges from the coupling of all these phenomena. Numerical simulations exhibit a highly non linear behaviour with respect to the governing parameters. We have identified two clearly distinct growth regimes: one regime that allows large growth heterogeneities by amplifying the effect of differences between cells, and conversely another regime that smoothes differences out and yields a homogeneous growth. On the biological level, the first regime is well adapted to morphogenesis, whereas the second one is well adapted to homothetic growth after the differentiated tissues have been created.