Nowadays, fuzz testing has significantly expedited the vulnerability discovery of Linux kernel. Security analysts use the manifested error behaviors to infer the exploitability of one bug and thus prioritize the patch development. However, only using an error behavior in the report, security analysts might underestimate the exploitability of the kernel bug because it could manifest various error behaviors indicating different exploitation potentials. In this work, we conduct an empirical study on multiple error behaviors of kernel bugs to understand 1) the prevalence of multiple error behaviors and the possible impact of multiple error behaviors towards the exploitation potential; 2) the factors that manifest multiple error behaviors with different exploitation potential. We collected <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">all the fixed kernel bugs</i> reported on Syzbot from September 2017 to January 2022, including 3,352 bug reports. We observed that multiple error behaviors manifested by kernel bugs are prevalent in the real world, and more error behaviors help unveil the exploitability of kernel bugs. Then we organized Linux kernel experts to analyze a sample of kernel bug dataset (484 bug reports, unique 162 bugs) and identified 6 key contributing factors to the mutiple error behaviors. Finally, based on the empirical findings, we propose an object-driven fuzzing technique to explore all possible error behaviors that a kernel bug might bring about. To evaluate the utility of our proposed technique, we implement our fuzzing tool <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GREBE</monospace> and apply it to 60 real-world Linux kernel bugs. On average, <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GREBE</monospace> could manifest 2+ additional error behaviors for each of the kernel bugs. For 26 kernel bugs, <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GREBE</monospace> discovers higher exploitation potential. We report to kernel vendors some of the bugs – the exploitability of which was wrongly assessed and the corresponding patch has not yet been carefully applied – resulting in their rapid patch adoption.