Odd that a 401(k) would not permit after-tax money from another 401(k) to be directly rolled over to that new 401(k). However, the tax code prohibits including any after-tax basis in an indirect rollover to a 401(k) and rollovers from IRAs to a 401(k).
Even if the after-tax basis can be directly rolled over from the old 401(k) to the new 401(k), it's almost certainly better to roll the after-tax basis over to a Roth IRA and roll over to the new 401(k) (or to a traditional IRA) only the pre-tax money from the old 401(k). The old 401(k) can do a direct rollover of the pre-tax portion, thus avoiding mandatory tax withholding, while distributing the after-tax basis to you which you can then deposit into a Roth IRA as a nontaxable conversion. The result would be zero tax impact.
Unless you waive the obligation, a 401(k) is required by law to provide you a description of your rollover options prior to making any distribution.
