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There is a widely held belief that future Radio Access Network (RAN) architectures will be characterized by increased levels of virtualization, whereby base station functionalities, traditionally residing at a single location, will be scattered across different logical entities while being interfaced via high-speed fronthaul (FH) links. For the deployment of such FH links, operators are faced with the challenge of maintaining acceptable radio access performance while at the same time keeping deployment costs low. A common practice is to exploit statistical multiplexing by allowing several cells to utilize the same FH link. As a result, in order to cope with the resulting aggregated traffic, different techniques can be used to reduce the required FH data rates. Herein, we focus on FH compression control strategies for multiple-cell/multiple-user scenarios sharing a common FH link. We propose various methods for sounding reference signal (SRS) handling and analyze different FH-aware modulation data compression and scheduling strategies. Considering a full system setup, including the radio and FH access networks, numerical evaluation is conducted using a 5G NR system-level simulator implemented in ns-3. Simulation results show that, under stringent FH capacity constraints, optimized modulation compression strategies provide significant user-perceived throughput gains over baseline strategies (between 5.2x and 6.9x). On top of them, SRS handling methods achieve additional 2% to 41% gains.