Parallel download protocols that establish multiple TCP connections to distributed replica servers have the potential to reduce file download time and to achieve a server-side load balancing. Unfortunately, parallel download protocols are also inherently unfair towards single-flow downloads and may even starve them. This paper presents TCP-ROME, a parallel download protocol that allows a dynamic mitigation of throughput and fairness. The key novelty is a receiver-based framework that allows a dynamic adjustment of the congestion and rate control of each subconnection. TCP-ROME offers two usage modes: a binary mode where the congestion control of each subconnection can be switched between a TCP-fair rate (high priority) and at a TCP-LP fair rate (low priority), and a more complex range mode where the aggregated throughput aims at meeting a specified target rate. Apart from the protocol specification, this paper develops novel analytical throughput models for TCP-LP and for TCP-ROME. The models are validated via simulations. Extensive simulation scenarios show the flexibility of TCP-ROME in mitigating performance for fairness.