A second appeal, or for that matter, any appeal is not a matter of right. The right of appeal is conferred by statute. A second appeal only lies on a substantial question of law. If statute confers a limited right of appeal, the Court cannot expand the scope of the appeal. It was not open to the Respondent-Plaintiff to re-agitate facts or to call upon the High Court to reanalyze or re-appreciate evidence in a Second Appeal.
Section 100 of the Code of Civil Procedure, 1908, as amended, restricts the right of second appeal, to only those cases, where a substantial question of law is involved. The existence of a substantial question of law is the sine qua non for the exercise of jurisdiction under Section 100 of the Code of Civil Procedure, 1908.
Hence you can proceed without waiting for the filing of second appeal.