Multi-tenant reduce number of MongoDB connections

Our multi-tenant app has about 4000 databases per tenant and we are having a problem with performance because of too many connections. Creating MongoDB connections on each database is a heavy operation. We tried the following approaches but still could not reduce the number of connections. 1. Sharding only applying for the datasets 2. Increasing the pool size already applied How to reduce the number of MongoDB connections? Is there any way to split databases into 1000,1000?