1. One who is in the midst of a Mitzvah:[1]

Anyone who is actively involved in a Mitzvah is exempt from wearing Tefillin throughout the entire day.[2] [This applies even by a Rabbinical Mitzvah[3], and even by a Shlichus Mitzvah, such as to raise money for captives or for a Kallah to marry.[4]] He is however obligated to wear the Tefillin for Shema and Tefilah.[5] This, however, only applies if one is not doing the Mitzvah during the time of Kerias Shema, if however one is doing the Mitzvah during this time then he is not required to stop for Kerias Shema or Tefila.[6] This applies even if the time of Shema and Tefila will pass. However, initially, it is forbidden for them to begin the Mitzvah near the time that Kerias Shema arrives.[7]

A Sofer Stam and their dealers: A Sofer Stam who does not work for the sake of profit[8] is exempt from wearing Tefillin throughout the entire day. This applies likewise for the Sofer dealers and the dealers of the Sofer dealers who purchase the Stam in order to sell them to those who are in need of them, that if they do not work for the sake of profit then they are exempt from wearing Tefillin throughout the entire day. However, they are obligated to wear the Tefillin during the reading of Shema and Tefilah.[9] This however only applies if the Sofrim are not writing Stam during the time of Kerias Shema, if however they are dealing with writing during this time then they are not required to stop for Kerias Shema or Tefila.[10] This applies even if the time of Shema and Tefila will pass. However, initially, it is forbidden for them to begin their work near the time that Kerias Shema arrives.[11] 

Guarding a corpse or digging a grave:[12] One who is guarding a corpse is exempt from Tefillin, Shema, Tefila and from all the Mitzvos.[13] This applies even though he is [physically] able to perform all the Mitzvos [during his guarding]. Likewise, one who is digging a grave for a corpse is exempt from all the Mitzvos. This applies even while he takes a rest from his work.[14]

One who is wearing Tefillin:[15] One who is wearing Tefillin is not exempt from fulfilling all the other Mitzvos. However, while he is putting on the Tefillin he is considered exempt from all the other Mitzvos.[16]

Found lost object:[17] One who found a lost object and is guarding it in his box is not exempt from fulfilling all the other Mitzvos.[18] The same applies for all cases of the like. [However, he is exempt from other Mitzvos while he is in the midst of dealing with the lost object as required according to Halacha.[19]]

Performing a Mitzvah that is of no trouble:[20] Even while involved in one Mitzvah and the opportunity to fulfill another Mitzvah presents itself, if he is able to perform both Mitzvos simultaneously, without any trouble or effort, then it is best to do so and fulfill both Mitzvos.[21]

[1] Admur 38:7; Michaber 38:8; Sukkah 26a

[2]Admur ibid; 71:4-5; 640:18; Michaber ibid; Sukkah ibid

The reason: The reason for this is because whoever is working the work of Hashem the Torah did not obligate for him to trouble himself and fulfill other Mitzvos even though he is able to do so. [Admur ibid]

[3] P”M 72 A”A 4; Yeshuos Yaakov 586:4; See Hisorerus Teshuvah 1:23 and Biur Halacha 72 “Im” that this applies even by a Hiddur Mitzvah

[4] See Admur 70:4 and 93:4 regarding Tzarchei Tzibur; Piskeiy Teshuvos 38:8 and 70:4

[5] The reason: This is required in order to accept the complete heavenly yoke and not testify false testimony on themselves. [Admur ibid] Vetzaruch Iyun, as once they put on the Tefillin for Tefilah why is it considered an extra effort to remain wearing them. Perhaps however this is because of Hesech Hadaas. Vetzaruch Iyun.

[6] Admur ibid; Rama ibid

The reason: If they began writing prior to the time of Shema, or transgressed and began writing after the arrival of the time of Shema, they are not required to stop to read Shema even if they have time to do their work after reading Shema, and the reading of Shema is a passing Mitzvah [i.e. Mitzvah Overes], nevertheless whoever is dealing with a Mitzvah is exempt from another Mitzvah even if he is able to perform both of them. The reason for this is because whoever is working the work of Hashem the Torahdid not obligate for him to trouble himself and fulfill other Mitzvos even though he is able to do so. [Admur ibid]

[7] Admur ibid and 72:2; M”A 38:10

[8] Admur ibid; M”A 38:8

The law if one’s intent is also for profit and also for Leshem Shamayim: Some Poskim rule that such a case is viewed as Lesheim Shamayim and he is exempt from fulfilling other Mitzvos. [Biur Halacha 38 “Hem”] Other Poskim rule he is not exempt unless he entirely does the work Leshem Shamayim. [Kesav Sofer 119; Aruch Hashulchan 38:11; implication of Admur ibid who omitted the word “main intent” which were written in the M”A ibid; See Chikrei Halachos 5:59; Sheyikadesh Atzmo ibid footnote 7; See Piskeiy Teshuvos 38:8 footnote 50]

[9] The reason: This is required in order to accept the complete heavenly yoke and not testify false testimony on themselves. [Admur ibid]

[10] Admur ibid; Rama ibid

The reason: If they began writing prior to the time of Shema, or transgressed and began writing after the arrival of the time of Shema, they are not required to stop to read Shema even if they have time to do their work after reading Shema, and the reading of Shema is a passing Mitzvah [i.e. Mitzvah Overes], nevertheless whoever is dealing with a Mitzvah is exempt from another Mitzvah even if he is able to perform both of them. The reason for this is because whoever is working the work of Hashem the Torah did not obligate for him to trouble himself and fulfill other Mitzvos even though he is able to do so. [Admur ibid]

[11] Admur ibid and 72:2; M”A 38:10

[12] Admur ibid and 71:4-5; M”A 38:10; Brachos 18a

[13] Seemingly, although he can technically do another Mitzvah while guarding, in which case it is best or even an obligation to do both, nevertheless perhaps he is still exempt being that its only when one can do two mitzvos within the same effort that we say that one should do so and not when it takes two different efforts.

[14] The reason: As even during his resting period heis considered to be dealing with a Mitzvah, as the purpose of his rest is so he can regain strength and return to digging. Therefore he is exempt during his break even though he is able to perform the Mitzvah. [Admur ibid]

[15] Admur ibid; Hagahos Ashri

[16] The reason: One who is wearing Tefillin, even though he is fulfilling a Mitzvah, is not considered dealing with a Mitzvah to be exempt from fulfilling all the other Mitzvos. He is only considered to be dealing with a Mitzvah while putting on the Tefillin, and not afterwards when he walks with the Tefillin throughout the day. [Admur ibid]

[17] Admur ibid; M”A 38:10; Ran

Other opinions: See Shaar Hatziyoin 470:38

[18] The reason: One who finds a lost object and guards it, even though he is fulfilling a Mitzvah, is not considered to be dealing with a Mitzvah to be exempt from fulfilling all the other Mitzvos so long as the item is in his box. [Admur ibid]

[19] Admur Metzia Upikadon 24

[20] Admur ibid; 640:18; Rama ibid; Ran

[21] Literally ” it is best for him not to be called evil”; Vetzaruch Iyun if this is an obligation or simply a Hiddur? From later its implied that it’s an obligation.

The reason: As the Sages only stated that that one is involved in a Mitzvah is exempt from another Mitzvah in a case that one needs to place additional due effort in order to perform the second Mitzvah. If, however, one can exert the same effort to perform both Mitzvos simultaneously, then he is to do so. [ibid]

[22] Shaar Hatziyon 470:39

[23] Shaar Hatziyon 470:39

[24] See Piskeiy Teshuvah 264 based on Or Zarua; Rameh 102