Multipath QUIC (MPQUIC) enables concurrent transmission over multiple paths, making it attractive to enhance the delivery performance of smartphones with multiple interfaces. Nevertheless, several issues in the current MPQUIC specification remain inadequately addressed. Congestion control in MPQUIC primarily relies on packet loss and favors paths with lower drop rates, which results in significant throughput degradation, especially in heterogeneous wireless networks with frequent random packet loss and varying path characteristics. Additionally, network fairness principles limits its performance, even in scenarios with independent and non-shared bottleneck paths. A final issue is that packet scheduling in dynamic and asymmetric paths poses a significant challenge, potentially causing out-of-order (OFO) arrivals and Head-of-Line (HoL) blocking if not appropriately managed. Inspired by Google’s BBR algorithm, this paper introduces a novel scheme called Shared Bottleneck and BBR-based Congestion Control (S2B2C) to address the above issues. It identifies subsets of subflows that share common bottlenecks within the MPQUIC connection based on the BBR’s internal mechanism. The scheme dynamically adjusts the pacing rate of these subflows to enhance goodput while preserving fairness with legacy single-path flows. Then, to mitigate inter-stream and intra-stream HoL blocking caused by OFO arrivals over asymmetric paths, we present a fine-grained Stream-path-bounded Priority-based Packet Scheduler (S2PS), which includes a stream dependency tree, a priority-based queuing, and a packet scheduling algorithm that uses a mixed-integer program formulation. Experimental results show that S2B2C achieves higher throughput while maintaining bottleneck fairness, and S2PS effectively mitigates HoL blocking with fewer OFO arrivals and shorter flow completion time compared to existing MPQUIC schemes in heterogeneous networks.