Yes, in fact you would have until July 15th, 2020, but you should contact your employer's payroll or Human Resource department so that they can designate the contributions as prior year.
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Are you self-employed? If not, no, you are not permitted to now make additional contributions to the plan for 2019. You are also not permitted to make regular personal IRA contributions to a SIMPLE IRA account. For regular personal contributions you can open a separate IRA account.
Even if you are self-employed, you were required by December 31, 2019 to make your election for any salary deferrals. Your required employer contribution for 2019 is determined by the requirements of the plan agreement established by October 1, 2018 or the date of establishment of the SIMPLE plan, whichever was later, the amount of your salary deferrals and the amount of your net earnings from self-employment.