I think it's better if you post the schematic of your circuit. However, i think you're talking about an integrated transconductor, isn't it? In this case, giving an high common mode input voltage will rise the low limit of your output swing (keeping in mind the basic transconductor amplifier n-type). You have to check your specifications. I hope i've been helpful!
if you are referring to you input common mode range (ICMR) limits, then i suppose they are basically determined from your architecture. So perhaps you want to have a look at your selected architecture and supplies !