The answer "No" is to the question, "Do I violate any rules."
However, if you are still working for any of these employers (or you are under age 59½ in the case of an individual 401(k)), you might be limited with regard to your eligibility to make distributions from the plan.
Also, you have the option to roll amounts from the traditional accounts in any of these plans directly to a Roth IRA rather than first rolling the money over to a traditional IRA. If any of the money in any of the traditional accounts in these plans is after-tax, it would potentially be advantageous to roll the after-tax amount directly to a Roth IRA and the pre-tax money to a traditional IRA in a split rollover permitted under IRS Notice 2014-54.
