May someone have both an IRA and a money purchase pension plan?

Does any law or regulation prohibit having both a personal IRA, or any sort of IRA, and participating in a money purchase pension plan simultaneously?

A person may have benefits in both an IRA and a money purchase pension plan at the same time. A person who accrues a money purchase pension plan benefit in a tax year may be prohibited from making a tax-deductible (or Roth) contribution to an IRA that same year. That depends on the AGI (adjusted gross income) level of the person (and perhaps spouse). See IRC section 219 for more details.