When a person loses a close relative (for whom he is required to mourn) and the relative has not yet been buried, the mourner is called an onen. An onen is exempt from performing positive commandments (mitzvot aseh) such as praying, putting on tefillin, and reciting Keriat Shema. However, he may not transgress any negative commandments (mitzvot lo ta’aseh).
Acharonim disagree as to his status when it comes to commandments that have both a positive and a negative component. For example, is an onen exempt from destroying his chametz before Pesach? On the one hand, this is a mitzva which requires taking positive action. On the other hand, destroying the chametz is also done to make sure that one will not transgress the negative prohibition of owning chametz (commonly referred to as bal yera’eh u-bal yimatzei).
An additional question pertains to an onen as well. May an onen choose to be stringent and fulfill the positive commandments from which he is exempt?
The answers to these questions depend upon the reason an onen is exempt from performing these. If the exemption is meant to give honor to the deceased and show that nothing else is important to the mourner at this point, then even if he wishes to perform these mitzvot he would not be permitted to do so. However, if the reason for the exemption is to enable the mourner to take care of the burial, then if he is able to arrange for someone else to take care of it (such as the local chevra kadisha), he would be permitted to perform these mitzvot. Alternatively, if the exemption is based on the principle that one who is already involved in performing one mitzva is exempt from performing another one (ha-osek be-mitzva patur min ha-mitzva), then if the mourner feels able to perform both mitzvot, he would be allowed to do so.
In Parshat Chayei Sarah, Avraham was an onen before Sarah was buried. Yet not only did he acquire a grave for her, he also purchased the field where the cave was situated, thus fulfilling the mitzva of Yishuv Eretz Yisrael (Settling the Land of Israel). Perhaps we may conclude that just as Avraham involved himself in additional mitzvot even while he was an onen, so too any onen who wishes may choose to perform the positive commandments from which he is exempt.