Great! Here's a fun example.

Let \\(A\\) be any set, and make it into a preorder by defining every element to be less than or equal to every other element. Do the same for some set \\(B\\). Then any function \\(f : A \to B\\) is monotone, because we have \\(f(a) \le f(a')\\) no matter what \\(a,a' \in A\\) are. Similarly any function \\(g : B \to A\\) is monotone. And no matter what \\(f\\) and \\(g\\) are, \\(g\\) will be be a right adjoint to \\(f\\), since

$$ f(a) \le b \textrm{ if and only if } a \le g(b) $$

(both are always true). Similarly, \\(g\\) will always be a left adjoint to \\(f\\).

This shows that when we make our preorders as far from posets as possible, right and left adjoints become ridiculously non-unique.

Let \\(A\\) be any set, and make it into a preorder by defining every element to be less than or equal to every other element. Do the same for some set \\(B\\). Then any function \\(f : A \to B\\) is monotone, because we have \\(f(a) \le f(a')\\) no matter what \\(a,a' \in A\\) are. Similarly any function \\(g : B \to A\\) is monotone. And no matter what \\(f\\) and \\(g\\) are, \\(g\\) will be be a right adjoint to \\(f\\), since

$$ f(a) \le b \textrm{ if and only if } a \le g(b) $$

(both are always true). Similarly, \\(g\\) will always be a left adjoint to \\(f\\).

This shows that when we make our preorders as far from posets as possible, right and left adjoints become ridiculously non-unique.