Is is common to solicit bids from other potential buyers even though we are currently negotiating on the acquisition of our startup?

Our startup is the process of being acquired. We're past the LOI, due diligence and have agreed on a price and terms. We haven't discussed a potential closing date yet. We aren't thrilled about the offer, but we've determined that it isn't feasible for us to continue our growth alone. We are passionate, experienced and love what we are doing but we all have little mouths to feed and aren't in a position to downsize and eat ramen noodles. We are late bloomers so to speak. I can't help but feel that it would make sense to reach out to other companies whose future plans may align with the space we are currently growing in but I have no idea if that's considered wrong. I'm the software engineer and I view this as the selling of anything else. To me, it would seem wise to at least see if anyone else would be interested since we never made it public to anyone that we'd even consider selling. This company flew me in under the pretense of potential partnership and bam, they surprised me with wanting to acquire us. The entire team feels very grateful but most of us feel like we'd regret not asking anyone else. So, would it be wrong to reach out to others and essentially convey that we are in the process of being acquired but if you're interested, we are entertaining offers?