Yes you can. I would follow this procedure:
1) Prepare all materials, and an additional large container to temporarily place the plant mid transplant.
2) Reach very gently with both hands at the same time, down the inside of the pot at the edge, using your fingers like a fork to gently tease the soil as you lower your hands, go as far down as possible.
3) Slowly and gently, and without the teasing motion, bring your hands together through the soil until they are approximately 20cm apart.
4) Very carefully and gently lift up the whole clump and plant, using both hands in the position you have carefully placed them.
5) Gently put the whole clump down onto/into the temporary container. *HELPFUL IF IT HAS SOIL IN TO REST IT ON*
6) Mix in the perlite and whatever else you wanted to to do adjust the soil in the pot.
7) Make a pit in the middle the correct size for the plant root clump.
8) Slowly and gently place the whole plant and clump back into the pot.
9) DO NO COMPRESS AT ALL.
10) Very gently and slowly water from the outside edges of the pot to the plant itself.
Good luck!