You can request as much life insurance as you want when you apply for a life insurance policy; however, the life insurance company decides how much life insurance they will sell you and for how much money.
So, they can say, no will will not sell you that much life insurance, because we feel you are a high risk, and do not want to take that risk insuring you for life insurance.
Many insurers may limit the amount of life insurance they offer applicants due to the applicant's health, age, lifestyle, occupation or hobbies.