User 25034 wrote "You can but then you need your group to be close and the background as far as possible (like as shooting in a path between trees) " and then AJ Henderson suggested that answer was not very helpful or clear.
Part of your original question was "If I really try, I can sometimes get the subject with a blurred background if I move in close (3ft) with a f/3.5"
There are a few competing things here.
First - your friend's lens has a maximum aperture of 1.8, vs your best aperture of 3.5. His larger aperture will result in a shallower depth of field, all else being equal. So you're already one notch down.
Second, you can only acheive 3.5 at the wide end of your lens - ie. 18mm - but this focal length will distort faces significantly. As others have mentioned, 70mm, 80mm and up over 100mm produce portraits that appear more realistic in facial proportions than using a wide angle. Therefore you will want to use the 55mm end of your lens as much as possible - however one of your comments suggests the aperture gets even smaller at that end of your lens - now you're two notches down on your friend's lens.
Third, depth of field is not only dependent on aperture; it is also dependent on the distance between the camera and the subject - the focusing distance. Take an example: If you got really close to the lined pages of a (paper) notebook, and took your shot at f3.5, you might expect 1 or 2 lines to be sharply in focus and the rest of the page pleasantly blurred (assuming you're looking along a page). These lines might be 1cm apart. Now imagine the same exercise in a carpark, looking down a row of cars. You might find 1 whole car is in focus. One car is definitely wider than 1cm, but your camera settings have not changed. The depth of field is dependent on the distance from you to your subject.
Therefore if you get closer to your subject, then your depth of field will reduce - but you want to avoid reducing your focal length below 55mm too, in order to avoid distortion in facial proportions. You're a little stuck here but read point four.
Fourth, and this is where the comment by User 25034 comes into play, imagine your subject (say a face) is really close to a wall (say the person is leaning against the wall) - even if you reduce your depth of field so that only the face is in focus, because the face is so close to the wall, the wall will still be highly recogniseable. However if you imagine the subject 5 steps away from the wall, now the face is crisp but the wall is so far away that it is really out of focus. Therefore while taking your shot, you could look for angles whereby the background is further away from your subject. This might mean a profile shot will give you a more blurred background - if that is the angle that results in the background being furthest away from your subject as is possible.
Note that regardless of the distance to the background, nothing changes in your aperture or in the distance between you and your subject, or in your focal length - hence this part of the photo (the face) will retain the same proportions / viewing angle, and the same sharpness and focus. Although your subject is not actually closer to you, it is relatively closer to you (compared to the wall) than when the person was leaning against the wall.
So to say in your question "if I move in close", it might be more helpful to think of it as "if I move in relatively close, compared to the background" - then yes, your photos will improve as you desire. Just remember, your kit is still starting two notches down compared to your friend's.