Two options. One is to login using new Microsoft account. Go to Settings, Accounts, Other Users and Add Other User (add new Microsoft account). Sign out, sign in with new Microsoft account.
The other option is to go to Settings, Account, Your accounts and to add your new Microsoft account there. If you want to install Office from Microsoft 365, open browser, go to https://m365.cloud.microsoft/apps/, login with new Microsoft account. You should have install option.
One more thing. If you will continue to use both Microsoft accounts, create separate profiles in your browser.