Can use mutli connection to create stream for client keepalive?

[vintmd]

go mod:
go.etcd.io/etcd/api/v3 v3.5.10
go.etcd.io/etcd/client/v3 v3.5.10

use way:
session, err := fm.etcdClient.NewSession(ctx, config.GetConfig().Etcd.SessionTTL) // 30s

appearance:
on one machine init one clientv3, concurrent maintain 6k session with TTL, if the session has done re-create new session to use. it always appears "session has done" exception.

question:
watch clientv3 code only use one connection stream send and recv each lease ID in order, I wonder if we can change the stream connection number to avoid client-side block？