Finding all marked elements using Grover's algorithm
After discussing the problem with some people from my institute that work on quantum computing, it turns out that one can augment the oracle to not provide elements that have already been found in previous iterations of the search. The trick is to modify Grover's algorithm as follows:

Say, we already know that 2 is an answer (from a previous iteration). After using the oracle to invert the phase of the marked elements within Grover's algorithm, we apply another operation that inverses the phase of the known answers again (thus cancelling the previous inversion for answers that are already known). Accordingly, the inversion about the mean in Grover's algorithm will not amplify the amplitude of these states.