Lava domes result from effusive eruption of high viscosity lava. These viscous lava extrusions range in shape from flat-topped domes with small height-to-width aspect ratios, to spine-like columns exhibiting large height-to-width aspect ratios. A primary control on morphology during early dome growth is thought to be the variation in rheological characteristics of extruded material. In this work, we present new scaled analogue models of lava dome growth that consider extrusion of a frictional plastic upper-conduit plug followed by viscous magma. We simulate the brittle plug using a sand-plaster mixture, the cohesion of which is varied by plaster content. We model the magma using sugar syrup, the viscosity of which is controlled by the weight percent of added crystalline sugar. The models both qualitatively and quantitatively reproduce part of the spectrum of natural dome morphology not previously obtained in most past analogue modelling studies. Model aspect ratios of 0.02 to 0.9 capture approximately 90 % of the reported aspect ratio variation in nature. Increasing plug cohesion results in extrusions with higher aspect ratios and spinier morphologies. Low viscosity fluid typically erupts through the brittle dome, whilst high viscosity fluid tends to promote endogenous growth or emerge as exogenous lobes. Particle Image Velocimetry shows that fracture localisation at the dome surface is cohesion-dependent, and eruption of fluid follows shear fractures within the dome. Where fluid remains contained within the dome, we see lateral spread leading to a wider and flatter dome morphology. Evolution of lava dome morphology, deformation, and associated hazards is guided by the complex rheological properties of the extruded material; we suggest that during episodic dome growth, these properties are largely defined in the conduit prior to their eruption.