We report studies of the growth of solid hcp 4He at pressures higher than the bulk freezing pressure using a cell design that allows us to inject atoms into the solid. Near the melting curve during injection we observe random events during which the pressure recorded in the cell drops abruptly. These events are accompanied by transient increases in the temperature of the cell. We discuss these transients and conclude that they represent the solidification of meta-stable liquid regions and the associated relief of strain in the local solid. We also observe that further from the melting curve the transients are no longer recorded, but that we can continue to add atoms to the solid, increasing its density at fixed volume. We document these changes in density with respect to changes in the chemical potential as a function of temperature and discuss these in the context of recent theoretical work.