Yes, you can! I've been in a Reading Spec position for several years, and have used both the push-in and pull-out method. I can tell you how I did each way.
For now, since I was asked to do the pull-out a couple of years ago, I'll discuss that way. I meet with groups of no more than 4 from the same grade level, but most likely different classes. I give them each a menu which is kept in my room As we choose strategies, I highlight them on the menu, and when the child gets to a point where they can do it independently, we put a check beside it. We may have 2 or 3 strategies we're working on at a given time.
After an quick review of a strategy most are working on, I start doing individual conferring with each for about 5-7 minutes or so. While I'm working with one student, the others are doing Read to Self, Listen to Reading or Word Work. I do set out the word work for them, based on what I noticed in their reading and writing. Listen to Reading is done on our Chrome Books--they may not finish a complete story, but can go back to it next time around.
As I'm conferring, I write notes in my CCPensieve, which makes it easy to send the notes to the classroom teachers (or to print them out weekly for teachers who don't use that tool).
I try to use as much of the same language as classroom teachers do with CAFE, so kids will see the connection between their classroom and our Reading Room.
Now, this is what a "perfect" day looks like, and we all know those are few and far between :), but we do try to get this structure down so we can work toward our goals.
Hope this helps a little bit. If you do a push-in program, I can share what I did then (which was definitely my favorite).