Yes, you can invest in both the 401(k) Roth and your individual Roth, assuming you meet the income limits for investing in the individual Roth. It is a great investing strategy, and you'll see the benefits with tax-free distributions at retirement.
One thing to consider - check to see if your employer matches the Roth 401(k) contributions in the same way as the non-Roth contributions. If not, factor that into your decision.
Best of luck!
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