8. Let the set $I=\{1,2, \cdots, 2 n+1\}\left(n \in \mathbf{Z}_{+}\right)$ have $k$ distinct subsets $A_{1}, A_{2}, \cdots, A_{k}$ that satisfy: for any $i, j(1 \leqslant i < j \leqslant k)$, we have $A_{i} \cup A_{j}=I$. Then the maximum value of $k$ is $\qquad$.
8. $2 n+2$.

First, the $2 n+1$ subsets of $I$ with $2 n$ elements and the $2 n+2$ subsets of $I$ satisfy the requirement.

Second, if $k \geqslant 2 n+3$, then among $A_{1}, A_{2}, \cdots, A_{k}$, there must be one with the number of elements less than or equal to $2 n-1$, let it be $A_{1}$. Then the $2 n$-element subset containing $A_{1}$ does not appear in $A_{1}, A_{2}, \cdots, A_{k}$ (otherwise, its union with $A_{1}$ would not equal $I$). Taking such a subset to replace $A_{1}$, the resulting $k$ subsets still meet the problem's requirements. By assumption, this process can continue indefinitely, but there are only a finite number of $2 n$-element subsets, which is impossible.
Therefore, $k \leqslant 2 n+2$.