Kate lifted one paw and swatted at Nick when he tried to chase her off, but she was careful not to get too playful for fear that they'd accidentally hurt Stiles.
When he found a compromise, it was acceptable to her and she flopped down on her belly, content to let him give them both some attention, at least for a few minutes. Eventually, she'd want to go and run a bit before Changing back, but this was kind of nice.