You can deploy a newer version of IE, best to use IE10 or IE11. The latest version of Chrome, Firefox and Safari (on Mac) supported by the vendor are also designed to work with Office 365.
TechNet: Office 365 System Requirements:
Office 365 is designed to work with the current or immediately previous version of Internet Explorer. We recommend that you upgrade to the latest version of Internet Explorer after it is released. Office 365 might continue to work with versions of Internet Explorer other than the current and immediately previous versions for some time after the release of a new version of Internet Explorer, but Office 365 can’t provide any guarantees.
When accessing Office 365 from older versions of Internet Explorer, users may experience known issues and limitations depending on the versions of Internet Explorer, including:
- Internet Explorer 9 Office 365 does not offer code fixes to resolve problems you encounter when using the service with Internet Explorer 9. You should expect the quality of the user experience to diminish over time, and that many new Office 365 experiences might not work at all.
- Internet Explorer 8 The user experience sending and receiving email with Outlook Web App and Internet Explorer 8 might be substantially diminished, especially when used on Windows XP or with low memory devices. Office 365 does not offer code fixes to resolve problems you encounter when using the service with Internet Explorer 8, and new Office 365 experiences might not work at all. You should also expect the quality of the user experience with Internet Explorer 8 to diminish further in the near future. After April 8, 2014, Internet Explorer 8 will only display Outlook Web App Light.