I have a Civil case against a contractor for breach of contract. The house is incomplete AND there are errors made in construction that may cost mor

Yes.  The case would cover all damages caused by the contractor's breach, inclduing both the additional money you will have to pay to complete the job for which the contractor was engaged and the damages caused by the errors (which can be either the cost to fix or the diminution in the home's value, depending on the exact facts.  However, there may be lower courts where jurisdiction is limited to under $25,000, or a similar sum, so you have to make sure that you sue in the right court.  You can't do this in small claims court, for example.