Given a number field $K$, is there a number field $L$ containing $K$ such that all prime ideals of $K$ are unramified in $L$?

Question

We know that there is no nontrivial extension $L$ of $K=\mathbb{Q}$ such that all the primes of $K$ are unramified in $L$ (The discriminant $\delta_L>1$).

Suppose that $\mathbb{Q}\subsetneq K$. Can we find an extension $L$ of $K$ such that all primes of $K$ are unramified in $L$ ?