Are Veterans eligible to collect both VA and SSA benefits at the same time? If so, is there a monthly cap?

Absolutely, Veterans who receive VA disability benefits may also receive SSA benefits, depending on the amount received from the VA and if they are approved for SSI or SSDI. 

SSI: VA benefits will affect the SSI benefit amount. SSA classifies VA benefits as “unearned income,” since it does not come from paid employment. As such, it will be deducted dollar for dollar from the SSI federal payment amount, after the general exclusion of $20. (All SSI recipients are eligible for this exclusion, where the first $20 of earned or unearned income is not counted against their SSI payment.)

SSDI: Alternatively, SSDI benefits are not affected by unearned income through VA benefits.

Please read more at SSA and VA Disability Benefits: Tips for Veterans.