Almost all insurance plans ask you to identify any other insurance policies you have that will cover you. They are making sure that they aren't both reimbursing for the same procedure. In cases where they do allow duplicate or overlapping coverage, they will want to coordinate benefits. You will have to ask both insurers if they allow this.
what If they disallow dual coverage, but you want to do so anyway? Making sure they don't know about each other would involve significant paperwork gymnastics. If the dentist knows you have a policy with X, they will frequently discount some procedures, but you would have to ask them not to do that for other procedures otherwise insurer Y would know you have a policy with somebody else. You would also have to always have the insurer reimburse you vs the dentist. This is not an advisable plan of action. If they disallow dual coverage and you try and do it any way, that would be insurance fraud.
If they do allow multiple policies, keep in mind that if the first policy is being purchased through your employer the $200 a year may only be a portion of the total cost of the policy. Many employers cover 50% or more of the group policy, so an individual policy not being paid by your employer could cost significantly more or not have as much coverage.