In PHPUnit, how do I indicate different with() on successive calls to a mocked method?

You need to use at():

$mock->expects($this->at(0))
     ->method('foo')
     ->with('someValue');

$mock->expects($this->at(1))
     ->method('foo')
     ->with('anotherValue');

$mock->foo('someValue');
$mock->foo('anotherValue');

Note that the indexes passed to at() apply across all method calls to the same mock object. If the second method call was to bar() you would not change the argument to at().