Continuing the effort to integrate the computer algebra system SINGULAR with the workflow management system GPI-Space, we will create a versatile and effective toolkit for massively parallel computations in algebraic geometry, providing full integration with OSCAR. Guided by applications to elliptically fibered K3 surfaces and to symplectic quotient singularities, we will develop a parallel framework for working with algebraic schemes. Results of the first funding period on computing integration-by-parts identities for Feynman integrals will be developed into a consistent massively-parallel framework for use in the high energy physics community.