The phrase "a further metaphor" is correct and usable in written English.
It can be used when introducing an additional metaphor to enhance or clarify a point being made.
Example: "In addition to the previous comparisons, I would like to present a further metaphor that illustrates the complexity of the situation."
Alternatives: "an additional metaphor" or "a supplementary metaphor".
In Obama's use, there is a further conceptual metaphor, the Actions Speak Louder than Words metaphor, in which Acting Is Forceful Communication.
What I want to think about, then, and hope we can talk about in class, is the way elaboration can be heaped upon elaboration, figure upon figure, the way an epic simile can set up a series of metaphors, the way metaphors themselves might host further metaphors, and the effect all this figuration has on syntax and grammar.
In the title of his memoir, The Diving Bell and the Butterfly, Jean-Dominique Bauby offered two further metaphors that captured, like Harmon's glass bubble, the claustrophobia of his condition as well as pointing to the possibility of escape.
Perhaps, a further concretization of this metaphor, away from its intersubjective anchoring, would make the statement close to a delusion.
This was a further indication that the 'program' metaphor of heredity was not merely superficial, but perhaps had a deeper meaning.
Virtual worlds are being used to understand spatial maps (Weisberg & Newcombe, 2015) and further body metaphor work is being done with motion capture sensors, like the Kinect, to teach students computer coding via dance moves (Parmar et al., 2016).
At the beginning of "Sexy Beast" a boulder rolls down a Spanish hillside and crashes into the hero's swimming pool -- a metaphor for the further bad luck about to ensue, but also for the reckless, risky, self-destructive possibilities of filmmaking.
"Breakfast Can Wait" is a slinky slow jam built around a food metaphor he takes way further than you expect.
Further — and this is key — a touch input metaphor and a pixel input metaphor must be wholly different and wholly incompatible with one another.
