21. Let $a$, $b$, $c$ be non-zero real numbers, and $a+b+c=0$. Then the value of $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{a b c}{|a b c|}$ could be ( ).
(A) 0
(B) $\pm 1$
(C) $\pm 2$
(D) 0 or $\pm 2$
(E) 0 or $\pm 1$
21. A.

Assume $a \leqslant b \leqslant c$.
Since $a, b, c$ are non-zero real numbers, and $a+b+c=0$, thus, $a<0$, at this time,
$$
\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{a b c}{|a b c|}=0 \text { ; }
$$

When $b>0$, $a b c<0$, at this time,
$$
\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{a b c}{|a b c|}=0 .
$$