Yes, there are adjustable,removeable screens in a frame that you can insert inside the window and in front of the outside screen to add a level of protection.
I lived in an upstairs apartment in Ontario and the screens pushed out far too easily. I didn't have air conditioning so needed to have the windows open in the summer just to keep the temperature at liveable level. I was worried about my cats pushing out the screens, so at the local hardware store I found these screens that are made in two sections on a metal frame that slide sideways to adjust to the width of the window the same way a child proof gate adjusts to the size of a doorway. They come in a variety of heights and as the width is adjustable they can fit virtually any window. Basically, you put them inside the window frame, open them up sideways to fill the window, then lower the inside glass so it rests on top of the screen insert.
I have been using them now for several years and brought them with me to our new home in Georgia. Now they go in the ground floor windows to prevent my cats from jumping or tearing through the screens and to prevent any visiting outside cat from making through-the-screen contact with mine.
I have seen the same thing available in Lowes and depending on the size you are looking from around $16 and up per screen insert. They are well made and well worth the investment if only for your peace of mind.