Yes, but it would be cumbersome and plain ugly. Writing scripts (i suppose you need it in a script) is all about clarity and making it easy to understand what is done, therefore you should do it in two steps using the expansions you already found. I would write it like this:
text="${text##*/}" # cut off the path
text="${text%.*}" # cut off the extension
For completeness' (but again: don't really do it! This is just to show off my prowess in writing incomprehensible code! ) sake: you can use an expansion inside another expansion as a pattern. For instance, this cuts off the first character in a string, notice the nested expansion:
chLine="abcdefghi"
while [ -n "$chLine" ] ; do
chChar="${chLine%${chLine#?}}" # nested expansion!!
chLine="${chLine#?}"
echo char is: \"$chChar\"
echo line is: \"$chLine\"
done
Using this device you could do what you want. Don't!