It is possible to design a multi-output network in Deep Network Designer, however it is not possible to train it using Deep Network Designer as training multi-output networks is not support with trainNetwork.
To train a multi-output network, you could build the network first using Deep Network Designer then export the network to workspace, then convert the layer graph to a dlnetwork and use custom training to train it.
Here is an example on creating a multi-output layer graph, converting the layer graph to dlnetwork then using custom training to train the multi-output network: