In-memory transactional data girds, often referred to as NoSQL data grids demand high concurrency for scalability and high performance in data-intensive applications. As an alternative concurrency control model, distributed transactional memory (DTM) promises to alleviate the difficulties of lock-based distributed synchronization. However, if a transaction aborts, DTM suffers from additional communication delays to remotely request and retrieve all its objects again, resulting in degraded performance. To avoid unnecessary aborts, the multi-versioning (MV) model of using multiple object versions in DTM can be considered. MV transactional memory inherently guarantees commits of read-only transactions, but limits concurrency of write transactions. We present a new transactional scheduler, called partial rollback-based transactional scheduler (or PTS), for a multi-versioned DTM model. The model supports multiple object versions to exploit concurrency of read-only transactions, and detects conflicts of write transactions at an object level. Instead of aborting a transaction, PTS assigns backoff times for conflicting transactions, and the transaction is rolled-back partially. We implemented PTS on Infinispan, and conducted comprehensive experimental studies on no and partial replication models. Our implementation reveals that PTS improves transactional throughput over MV-Transactional Forwarding Algorithm without PTS and a scalable one-copy serializable partial replication protocol (SCORe) by as much as 2.4× and 1.3×, respectively.