I must agree with Walter on everything he said. Offering more does not guarantee you will win the bidding war. The seller is in distress and for them the most important thing is to accept an offer that's almost guaranteed it will close.
First, yes you can increase your offer. Talk to your agent and let the listing agent know your intent. That said, cash offers are tough to compete against. The strength of your offer including downpayment and credit scores will effect the decision. In addition, the appraisal needs to be consider. If you bid higher and the property has a chance to NOT appraise at that amount, it might not help.