How many Transport Clients can a Elasticsearch cluster have?

The transport client is a normal client, it doesn't join the cluster or anything like that. That said it is recommended that the transport client is a singleton in your application, it is thread-safe hence the same instance should be used for all your requests to elasticsearch. The problems that may arise from using more instances are more on the client side though than on the server side. Maybe too many connection handles also on the server side.