If you feel like doing some hex-editing, it's the third byte in the OBJECT file. The value you need to put there depends on whether your OBJECT file is encrypted or not.
If your current limit is sixteen objects, then the value of the third byte will be 10 when you open it in a hex-editor if the OBJECT file is not encrypted. If the OBJECT file is encrypted, then the third byte will be 79.
To figure out which value to put there, the easiest thing to do is use the system's calculator if you're using Windows. Put the number of animated objects you want in decimal format (maximum of 255), then click the radio button that says "Hex". If the OBJECT file is not encrypted, just type the value that you see now into the hex editor as the third byte in the file. If the OBJECT file is encrypted, you need to xor the value against the ASCII value for the letter i (69 hex). Hit the button that says "Xor" and type "69" and hit "=". The result is the value that you need to change the third byte to.
For detailed information about the OBJECT file format, see the AGI Specs.