If one began blowing the Shofar and is unable to complete the entire set of 30 blows a second person can take him over and complete the remaining blows. If the second person could not complete the remaining blows then a third person is to take him over and complete the remaining blows. This applies so on and so forth as there is no maximum limit for how many people can be involved in the blows [and hence even if 27 people blow one blow each the Mitzvah is fulfilled].
Should the substitute repeat the blessing? The substitute is not to repeat the blessing prior to blowing as he has already fulfilled his obligation with the blessing said by the first blower. This applies even if the first blower did not manage to blow even a single blow, and was then substituted, nevertheless his blessing is not considered to be a blessing said in vain. However if the substitute blower was not present at the time of the blessing [and he desires to fulfill his obligation with the current blowing] then he must [silently] repeat the blessing prior to blowing being that he did not fulfill his obligation with the first blower. If however the substitute already fulfilled his obligation through hearing all the blows in a different area then he is not required to repeat the blessing prior to blowing being that the listeners already heard the blessings from the first blower.
One may have another person substitute him in middle of a set if he is unable to complete the blows. If the substitute did not hear the blessing from the first blower then he is to repeat the blessing if he intends to fulfill his obligation with this blowing.
If one did not yet hear any of the blows and he is taking over the Baal Tokeia is he to restart from the first blow?
If he desires to fulfill his obligation with this blow then he is to start from the beginning. However Bedieved even if he did not do so he fulfills his obligation if he makes up the missed sounds after completing the blows for the listeners.
A Segula for a “broken” Shofar:
If one is not being successful in sounding the blows from the Shofar it is a Segula to turn the Shofar around and recite the psalm of Vayehi Noam into the mouth of the Shofar. This was experimented in a certain synagogue and the Shofar began to sound the proper blows.
 585/8-9; 590/14; Michaber 585/3; R”H 34b
 However a single blow can never be split to two people such as having one person blow one shever and another blow two shevers.
 This is not similar to the Torah reading in which case the person taking over must start from the beginning as by the Torah it says Torah Temima. [M”A 585/6; see Michaber 140/1]
 585/8; As he had in mind to fulfill the obligation of all the listeners. Hence the second blower, as well as the entire congregation which heard his blessing [are still covered by that blessing and hence], are not required to repeat the blessing. [ibid]
 585/9; M”B 585/11 in name of Elya Raba; This case refers to a case that the first blower did not manage to blow even a single blow and he hence is blowing thirty blows for everyone to hear. [See however Admur 263 KU”A 5 that it is a Dochek Gadol to establish this to be the case and hence one must say the following alternative:] Alternatively it refers to a case that he arrived in middle and will be re-blowing from the beginning, or will make up the blows he missed after he finishes blowing for the listener. See Q&A!
 M”B 585/11; Chayeh Adam 141/8; Kaf Hachaim 585/34; Seemingly the reason for saying the blessing silently is in order to not require the listeners to answer Amen to his blessing and hence cause them to make an interval between the blows.
 585/9; Olas Shabbos 585/2; Chok Yaakov 432/11; Peri Chadash; Shulchan Gavoa 585/5; Erech Hashulchan 585/4; Mamar Mordechai 585/3; Bigdei Yesha; Derech Hachaim 4; M”E 585/8; M”B 585/11; Kaf Hachaim 585/34
Other Opinions: Admur rules in 263/15 that there are opinions which rule that whenever an emissary is fulfilling a Mitzvah on behalf of another person he is to say a blessing [if he did not hear the blessing from that person], even if the sender already recited a blessing and began the Mitzvah and the emissary has already fulfilled his obligation. Thus in this case the substitute of the first blower is to recite the blessing even if he already fulfilled his obligation or arrived in middle of the set. The reason is because the substitute is obligated to assist other Jews to fulfill Mitzvos due to the law of guarantors [Areivus] and what difference does it make if one is personally commanded to do a Mitzvah for himself or is commanded to do so on behalf of another, either way it is a Mitzvah that requires a blessing. Admur proves this opinion from the Beis Yosef 585 which rules that if the substitute did not hear the blessing he is to repeat it, and the Michaber does not differentiate between whether the substitute is currently fulfilling his obligation or not. Practically in 263/15 Admur rules that the custom is to be lenient regarding Hadlakas Neiros that the emissary can recite a blessing even if the mother of the house already recited a blessing and lit candles in one area. However regarding Shofar and Bedikas Chameitz [see 432/9] since there is no set custom to be lenient Admur rules like the stringent opinion which forbids the repetition of a blessing by the emissary if he is not currently fulfilling his obligation. [263 Kuntrus Achron 5] See also Kaf Hachaim ibid
 Elya Raba 585/12; Chayeh Adam 141/8; M”E 585/8; Kaf Hachaim 585/35
 M”A 585/11 in name of Mateh Moshe and Mahril brought in M”B 585/31; See Chapter 3 Halacha 3