Found Stray/Abandoned Cat. Shelters are full. Any options?

This cat came up to me meowed and rubbed against my legs. I've been calling all morning for different shelters but all are full. No microchip, not sick but is very very skinny. I don't want to release him back outside but I can't keep him for very long. I saw pet furniture in the alley about a month ago and my hunch is he was abandoned in the move. He is so friendly. Are there any other options?