Put Resident Cat (RC) on the back patio and New Cat (NC) inside the play area and closed the sliding-glass door. RC hissed and batted at the glass; NC put her ears down and hissed.
Observed the two cats had no problem at a distance; when they got close, they got riled-up.
Put NC in room with RC’s litter box and water; put RC in master bedroom/bathroom with NC’s litter box and water so they could get used to each other’s scent. RC hissed once.
Tried feeding RC and NC at opposite ends of a hallway; NC approached RC and RC ran away. Put up makeshift bars from the frame of a baby crib to separate the two; they batted at each other through the gaps.
Separated RC and NC via French-style doors between the play and dining areas; NC stuck her paws under the door and actually started playing with RC.
Put up a section of 5-foot tall chicken wire in the doorway between play and dining areas, with a cat on either side so each can see and smell, but not touch, the other. Despite some hisses from RC, the two cats seemed to want to play with each other.