Is it ok to get multiple commitment letters from multiple lenders for morgage loan?

I already got approved for a morgage loan from a lender. I also have applied to other lenders, and a bank would do appraisal tomorrow and the branch manager has told me that there’s high probability to be approved for the loan.

However, the first company which already approved the loan recognized that I was trying other lenders, then, the company is pushing me to get my credit card information and is hurrying to issue commitment letter. The company want me to tell the bank stop proceeding. The company also want me to pick up the commitment letter as soon as it is ready and tell the seller’s attoney that I get the commitment letter from the company.
However, since the loan offer, which means both interest rate and closing costs, is better with the bank. So, I want to wait more until I get approval and commitment letter from the bank.

Is it ok to get commitment letter from both parties in my hand? Any legal obligation? Any penalty? Anything to be careful?

Thanks for help!

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