Is it permissible to suffice with two rak'ahs in the supererogatory prayer of Dhuhr if I intended four rak'ahs but did not have time to complete them?

It is established that the Sunnah prayer associated with Dhuhr (midday prayer) consists of two rak'ahs before it and two rak'ahs after it. In another narration, it is four rak'ahs before it and two rak'ahs after it. And in yet another narration, it is four rak'ahs before it and four rak'ahs after it. If there is ample time before the obligatory prayer, you may pray the Sunnah prayer as four rak'ahs. If time is short, you may shorten it to two rak'ahs. There is no strict requirement to specify the exact number of rak'ahs for the Sunnah prayer you intend to pray, but it is essential to have the intention to pray when you begin. It is permissible, according to some scholars, to make up for a missed Sunnah prayer if it was missed.