R.J.
I have had cats for about 15 years and integrated cats into the home. There are a couple scenarios to deal with and a couple of options.
First, make sure you have 2 sets of everything in different areas of the house. 2 litter boxes, 2 food dishes, 2 water bowls, 2 different sleeping areas, and 2 scratching posts. Your Calico feels threatened and it could take her/him up to 6 months to adjust.
Are both cats fixed and are they the same sex?
Sometimes cats don't get along like people. I had Jax, got Charley off the street, and Charley was terrified of Jax. Within a few weeks we brought in a female, she got attached to Jax-like he was hoping to have with Charley and Charley became the loner-he was very pleased being left alone. Sometimes it takes a 3rd cat to separate the issue.
The other thing, you may want to keep the new kitty isolated to a room or area of the house for a few weeks and slowly introduce the two for a few hours each day....tossing new kitty into the mix is a HUGE threat to Calico.
Talk to your vet, they can help too.