Is it possible to specify both upper and lower bound constraints on type parameters in Java?

I don't believe so - as far as I can tell from the language specification, "super" is only valid for wildcard types in the first place. The syntax for wildcards also suggests you can only have one wildcard bound, too - so you can't use something like this either:

// Invalid
void foo(List<? extends Foo super Bar> list)

Even though both of these are okay:

// Valid
void foo(List<? extends Foo> list)

// Valid
void foo(List<? super Bar> list)

As noted in comments, it's possible to have multiple upper bounds - but only for type parameters and cast expressions. For example:

// Valid
<T extends Number & Comparable> void foo(List<T> list)

From Oracle's tutorial:

Note: You can specify an upper bound for a wildcard, or you can specify a lower bound, but you cannot specify both.