In general (in the US) they can.
Again generally speaking, businesses pay taxes on net income — income minus expenses. Some businesses will do speculative things with their income (expand the business, try new ideas, etc) in order to have their net income be as close to zero as possible and thus not pay income taxes (they will still pay other forms of tax such as employment taxes). The tax code is built to encourage this in order to spark business growth and development (usually to get more people hired and thus more employment tax and other economic system benefits).
Most companies don’t use this tactic because “most” companies exist to make a profit. They choose to not hit that 0 net profit and instead pay the taxes on the business income and record what’s left as profit for the owners.
Tax deductions count against taxable income, not the total taxes paid. Businesses do deduct all of their expenses from their income, they only get taxed on the difference, which is profit. If your expenses are more than your income, you made no money and don’t pay tax. There are ways to deduct more from your income, e.g. deferring losses from one tax period to another.
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