This paper describes BigBFT, a multi-leader Byzantine fault tolerance protocol that achieves high throughput and scalable consensus in blockchain systems. BigBFT achieves this by (1) enabling every node to be a leader that can propose and order the blocks in parallel, (2) piggybacking votes within rounds, (3) pipelining blocks across rounds, and (4) using only two communication steps to order blocks in the common case. BigBFT has an amortized communication cost of $O(n)$ over $n$ requests. We evaluate BigBFT's performance both analytically, using back-of-the-envelope load formulas to construct a cost analysis, and also empirically by implementing it in our PaxiBFT framework. Our evaluation compares BigBFT with PBFT, Tendermint, Streamlet, and Hotstuff under various workloads using deployments of 4 to 20 nodes. Our results show that BigBFT outperforms PBFT, Tendermint, Streamlet, and Hotstuff protocols either in terms of latency (by up to $70\%$) or in terms of throughput (by up to $190\%$).