Multi task learning in Keras
By using the functional API you can easily share weights between different parts of your network. In your case we have an Input $x$ which is our input, then we will have a Dense layer called shared. Then we will have three different Dense layers called sub1, sub2 and sub3 and then three output layers called out1, out2 and out3.

x = Input(shape=(n, ))
shared = Dense(32)(x)
sub1 = Dense(16)(shared)
sub2 = Dense(16)(shared)
sub3 = Dense(16)(shared)
out1 = Dense(1)(sub1)
out2 = Dense(1)(sub2)
out3 = Dense(1)(sub3)


We can define our model now like this:

model = Model(inputs=x, outputs=[out1, out2, out3])


It will expect a tuple/list of three elements now, one for each output.

You can go a lot further with these concepts. Let's say we would like to learn individual weights for the person layers but still want to have the same weights for the linear combination towards the output layer, we could achieve that by doing this:

out = Dense(1)
out1 = out(sub1)
out2 = out(sub2)
out3 = out(sub3)


EDIT: Concatenating is basically the opposite of what you want to do, it's pasting (intermediate) outputs of different parts of your network into a new layer. You actually want to split off to multiple different parts.