I retired at end of Q1 2013 at age 64. I immediately started drawing monthly distributions from my 401(k) plan.
Would it be possible to transfer the balance of this 401(k) to another 401(k) or some other form of retirement plan?
Most 401(k) plans do not accept rollovers from participants that are not active employees. You can contact the plan administrator for a distribution form that will allow you to open an IRA or another qualified account and roll the funds directly into that account. If you open an account with Fidelity or Vanguard, they can help you with the paperwork.
As Nathan mentioned, you can transfer to an IRA.There are a number of reasons to do this, a partial transfer also being an option.
Regarding the last point, consider, in 2017, taxable income for a couple, $75,900 (implying gross of $96,700) would be taxed at $10,452. But the mandatory 401(k) withhold is 20% or $19,340. Easy to use the IRA, take withdrawal during the year, and just withhold tax in December, when you can estimate tax burden to the nearest $100.