DAY is a hinge word: 6 words make a compound in front of it and 5 make one after it, so it can sit in the middle of a chain and hold two compounds together at once.
Each of these makes a compound ending in DAY.
Each of these makes a compound starting with DAY.
DAY is a unit of time and a name for daylight, and both senses hinge. BIRTHDAY and PAYDAY pick out a particular day; DAYLIGHT and DAYBREAK are about the light itself.
Put any word from the first list in front and any word from the second behind, and you have a three-word chain in which both neighbouring pairs join. Here are some of them.
BIRTH → DAY → BREAK — birthday and daybreakEVERY → DAY → DREAM — everyday and daydreamPAY → DAY → DREAMING — payday and daydreamingSOME → DAY → LIGHT — someday and daylightSUN → DAY → TIME — sunday and daytimeKEYSTONE is a free daily puzzle built entirely out of chains like these. You get the two ends and have to fill the two words in the middle. Three bridges a day, no account, no cookies.
Each of these has a page like this one. There is also an index of all 28.
BACK · BALL · BED · BOARD · BOOK · BREAK · DOWN · FALL · FIRE · GUN · HAND · HEAD · HOUSE · LAND · LIFE · LIGHT · MAN · NIGHT · OFF · OUT · OVER · SHIP · SIDE · SOME · TIME · WAY · WORK