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We prove joint universality theorems on the half plane of absoluteconvergence for general classes of Dirichlet series with an Euler-product,where in addition to vertical shifts we also allow scaling. This generalizesour recent joint universality results for Dirichlet $L$-functions. In contrastto classical universality, we do not need that the Dirichlet series in questionhave an analytic continuation beyond their region of absolute convergence. Alsowe may allow weaker orthogonality conditions for pairs of Dirichlet series thanin the previous joint universality results of Lee-Nakamura-Pa\'{n}kowski. Wetake care to avoid using the Ramanujan conjecture in our proof and hence as aconsequence of our universality theorem, we obtain stronger results on zeros oflinear combinations of $L$-functions in the half plane of absolute convergencethan previous results of Booker-Thorne and Righetti. For example as aconsequence of our main universality result we have that certain linearcombinations of Hecke $L$-series coming from Maass wave forms have infinitelymany zeros in any strip $1<$Re$(s)<1+\delta$.

Joint universality on the half plane of absolute convergence