SOLUTION
| 1 | 2 | 3 | 4 | ACROSS |
| C | C | C | C | 1 Prophesies [foresees] |
| A | A | A | A | 2 Raids [forays] |
| T | T | T | T | 3 Roaring ocean region [forties] |
DOWN
1 Kind of scan [CAT scan]
2 Kind of tractor [Caterpillar]
3 Either of two kinds of boat [catamaran or catboat]
4 Kind of barbelled fish [catfish]
All usages of CAT/Cat/cat are in Marriam-Webster (as is “Roaring Forties”, which to be honest was new to me). There’s enough other senses of “cat” that I could easily have made this a 3×7 rectangle if only there were a reading of AAAAAAA to go with “Seven Seas” and “seventies”! (Though George Barany notes that this would also remove the fortuitous link with the puzzle's (post factum) title, which exploits the fourth-month date of April Fool's.)