I have been incorrectly assuming that statements made by Zhuangzi originated with him and are thus expressions of his own point of view. But now Wu (The Butterfly as Companion) has suggested that these are quotes from sophists only given with a view to deconstructing them. I have taken what Zhuangzi offers only for the purpose of critiquing them, to be what he actually believed. But did he believe them or not? Yes. And no.
He adapts Hui Shih's "Love all things without exception, for heaven and earth are one body" and possibly (though no sophist) Mencius' "All things are complete in me" (Mencius 7A4) to read: "'Heaven and earth, with I-myself are born-at-the-same-time,' and 'Myriad things with I-myself make one'" (Wu).
Concerning the “oneness” of things, Zhuangzi immediately demonstrates that by positing oneness one necessarily destroys it: “Now-that they have already been 'made one', does the word still, indeed, obtain its existence? . . . The one with the word make two; two with the word make three" (Wu; italics mine) Oneness cannot be demonstrated because the act of doing so posits two; and once you've got two, you're soon back to myriad things. If oneness can be demonstrated by adding things up, then diversity can be demonstrated by dividing things out.
So does Zhuangzi believe in oneness? Yes. But we cannot make one that which already is one. "To labor one's mind trying to make things one," Zhuangzi tells us, is to be like monkeys who cannot see the overall numerical unity of chestnuts however distributed; three now and four later is ultimately no different from four now and three later.
Hui Shih thought he could demonstrate oneness logically (even if the logic was used to deconstruct itself), but in doing so he could not psychologically participate in the oneness that already is. Mencius thought that by being morally pure he could obtain that oneness, but by making Dao moral, that is discriminating, he destroyed every possibility of oneness and any participation in it. If there is oneness, it is already unconditionally so.
Zhuangzi agrees with the arguments of the sophists but turns them around on themselves. Demonstrate oneness and you void it. To try to logically or morally make things one renders the experience of oneness impossible. Take a step back, he suggests, shine a light on both sides of the coin (oneness and diversity) and accept them both as one coin, one reality. Affirm the one by embracing the many. Affirm the many by embracing the one. How does one express oneness? "Only follow-on the 'this-yes' of all" (Wu). Or, as Ziporyn has it, "Follow along with the rightness of the present 'this'." Or, as Zhouzi would put it, "All is well! Whatever is or happens is 'right' for you." Realize that not-one is also one and, therefore, oneness is already unconditionally true of you.
You can check out Scott's writings on Zhuangzi here.