Solid-state drives (SSDs) are widely used in cloud storage. As the capacity of an SSD has been increasing, it has become common for many virtual machines (VMs) to share a single SSD to maximize resource utilization. However, this sharing can degrade the efficiency of internal operations, such as garbage collection, resulting in increased latencies. Existing literature in this field has mostly focused on inter-device isolation considering the storage device as a black-box entity or presumed an SSD to be shared by up to only eight VMs. In this study, we first analyze a realistic SSD usage environment in cloud systems and identify that block-level data isolation (BDI) should be guaranteed to efficiently scale up the number of VMs in an SSD with minimum latency increases. However, previous schemes cannot work efficiently with BDI when the SSD is shared by dozens of VMs. Based on this analysis, we propose an SSD internal resource management scheme in a cloud environment, called highly VM-scalable SSD (VMS). VMS dynamically partitions physical resources and allocates them to VMs, while the VMs share global buffer blocks to lower latency during abrupt fluctuations of write I/O intensities. Our experimental results show up to 29% of latency reduction. VMS exhibits reduced latencies even in the experiment with 64 VMs, where existing schemes do not function normally.