3 open credit cards. Should I switch to a 0 percent card?

If I only have 3 open credit cards and one is offering a 0 percent interest. I would like to transfer the balances to one card. Would that cause a significant drop in my credit score? Because then I would only have one open line of credit. Is it best to just keep them separate. I have tried to get the credit card company to lower the interest rate but they will not do so.
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I "hop" credit card interest rates my self.
do it but only use 75% of your total high credit limit
if get a credit limit of 15,000 dollars do not use more that
15,000X .75 = 11250. I have to remember most credit card companies charge a .03 balance transfer fee on each transaction. That's why I say 75% rather than 80% for my credit limit ratio. If I pay the fee up front and I get 0 percent for like 6 months my total monthly obligation goes down because the payment has less interest built in. Many times I can quailify for another card when 6 months run out because my debt to income ratio goes down when I pay mostly on priciple. The main thing is lower my prinicple by paying less interest

On the down side of credit scores I must remember it will take 12 months for my new credit line to get rated.
On the upside my credit card I am giving up is rated too so My score should not be affected to much in most cases where I keep good credit and less than 80 ratios.