We present an electromagnetic model describing liquid-core liquid-cladding optical fibers sustained by light radiation pressure that encompass the contribution of all the allowed propagating modes. Various sequences of unstable and stable equilibrium liquid column diameters are found above a threshold power. The non trivial relationship between single or multi-valued column diameter with a mono- or multimodal structure of the electromagnetic field is analyzed and the influence of the light-matter interaction geometry is estimated. Moreover, we propose a geometrical interpretation based on a ray optics approach that brings an intuitive understanding of the role played by higher order propagation mode in the occurence of a multistable liquid-core behavior.