In a Keynesian model with a foreign sector, an increase in the domestic income level will .

In a Keynesian model, imports are considered a function of domestic income. As domestic income rises, consumers and businesses have more disposable income, leading to an increased demand for goods and services, including those produced abroad. Therefore, an increase in domestic income leads to an increase in imports.

Exports are primarily determined by the income levels of foreign countries and the exchange rate, not by the domestic income level. Changes in a country's own domestic income do not directly affect the demand for its goods by foreign buyers. Therefore, exports remain unchanged when domestic income increases.

An increase in the domestic income level will leave exports unchanged and increase imports.

The final answer is $\boxed{\text{b. leave exports unchanged and increase imports.}}$