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In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field $F$. We do this for automorphic representations of an arbitrary reductive group $G$ over $F$, which is compact at infinity. In the special case where $G$ is an inner form of $\mathrm{GSp}\left(4\right)$ over $\mathbb{Q}$, we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.