Medicare Economic Security Solutions Act This bill modifies provisions relating to enrollment periods for Medicare medical services. Among other things, the bill establishes a late enrollment penalty of 15% of monthly premiums and applies the penalty for a period equal to twice the number of months in each 12-month period during which the individual was not enrolled. Currently, the late enrollment penalty is 10% of monthly premiums for each 12-month period during which the individual was not enrolled, and the penalty continues to apply for as long as the individual is enrolled in Medicare medical services. The bill also expands the special enrollment periods to individuals who have health insurance coverage other than through their employer.