Can a participant who receives the maximum contribution allowable to a defined contribution plan make contributions to a traditional or other IRA?

Yes. The IRA Contribution dollar limit is not affected by the active participation in a qualified plan. However, deductibility of the contribution for the individual is determined by their Adjusted Gross Income. See IRS Pub 590.

Contributions to a non-deductible traditional IRA are always permissible. Whether the client can make a contribution to a Roth IRA depends on his, hers or their MAGI for the year. It is unlikely that a client receiving a maximum allocation in a defined contribution plan would be below the MAGI threshhold for a deductible traditional IRA.