In this talk, we wii discuss the construction of infinitely many H\older continuous global-in-time solutions to the stochastic Euler equations in the space $C(\R;C^{\vartheta})$ for $0 < \vartheta < \frac{5}{7}\beta$, with $0 < \beta < \frac{1}{24}$. A modified stochastic convex integration scheme, using Beltrami flows as building blocks and propagating inductive estimates both pathwise and in expectation, plays a pivotal role to improve the regularity of H\older continuous solutions for the underlying equations. As a main novelty with respect to the related literature, our result produces solutions with noteworthy H\older exponents.