I went up to Effects>Texture and can't add another texture. The trash and + are greyed out. Why?
You can apply additional effects via the appearance panel.
Without seeing your layers panel it is hard to determine why this is happening. You should be able to add another effect via the effect gallery. Is the object selected? But as @MonikaGause suggested, a great way to work is by using the appearance panel and adding additional effects there.
You were able to add effects inside the Effect Gallery back in Version CS2 when Filters still existed.
Since Filters were taken away and there are only effects left, you cannot add effects from inside the Effects Galery.
Great! I went this route and was able to add several. Thanks!