I am looking to buy a house. Rather than using different agents, can I get one agent to show me all the MLS listings that we are interested in? Will this affect commissions and the acceptance of my offer?

For example, one of the homes is listed with Century21 at $80,000. I have been getting a Coldwell Banker agent to show us homes. She seems honest and I like her. I am not sure how commission splitting works. If the Coldwell agent shows me this Century21 listing, will they be less likely to accept my offer? I plan to offer $70,000. Should I go ahead and get the Century21 agent to show me the home? Would this increase the chance that my offer is accepted, since that would increase the commission for the Century21 agent (since he would not have to split it with the Coldwell agent). Sorry if this sounds confusing. I would appreciate any help or advice, if you can understand what i am asking. Thank you.