BGN encryption scheme with unbounded message space
There is a scheme whose purpose is exactly that, the LWE-based BGN-like encryption scheme. In general, we do not know how to achieve large message space for homomorphic encryption using discrete-log-style crypto; all known current solutions require lattice-based cryptography.

EDIT: reading the comments on your question, it seems you want to leak only whether the output is zero or not, by masking with a large random $r$ multiplicatively. But the standard BGN cryptosystem already allows that: the parties can always decrypt $g_t^{\mathsf{DFN(x)}}$ with BGN ($g_t$ is a generator of the target group), only the discrete logarithm at the end requires the message space to be small. However, seeing $g_t^{r\cdot\mathsf{DFN(x)}}$ for a large random $r$ already allows to see efficiently whether $\mathsf{DFN(x)} = 0$ or not: if it is equal to zero, then $g_t^{r\cdot\mathsf{DFN(x)}} = 1$; otherwise, $g_t^{r\cdot\mathsf{DFN(x)}}$ is just a random group element since $r$ is random.