Yes, a couple can each have a claim in their own right.
If both claims are PRSI-contribution based (e.g. 2 x Contributory State Pension), then they will each receive the maximum rate if they have enough contributions.
If one of the claims is means-tested then the maximum rate might not be paid on that claim - it depends on the means. In your example, disability allowance is means-tested.
There is also a "maximum pay" limit - for example, if a couple are both signing on, one on Jobseeker's Benefit (PRSI-based), the other on Jobseeker's Allowance (means-tested), the couple cannot be paid more on both claims than they would get if only one of them was claiming.