Is it possible, without closing it, to transfer funds from one existing channel to another?
The Lightning Network is a network of routed payment channels. You can transfer funds from one channel to another by finding a route and adjusting the balances of the channel participants along the route. This only changes how the fixed capacity of channels is distributed in a channel.
You can not at the moment increase or decrease the capacity of a payment channel on the fly. This is technically feasible though, and is being worked on as part of the BOLT specifications effort. This is called splicing.