The phrase "additional contentions" is correct and usable in written English.
It can be used when referring to extra arguments or claims that support a particular position or viewpoint in a discussion or debate.
Example: "In addition to the main argument, the author presents several additional contentions to strengthen their case."
Alternatives: "further arguments" or "supplementary claims".
His lawyers had continued to advance additional contentions until December, when Mr. McVeigh told the trial judge, Richard P. Matsch, that he wanted to stop his appeals.
S/he must refute every contention of side government, rebuild all of side opposition's contentions and introduce any additional contentions s/he wishes to add.
S/he must refute every contention the Member of the Opposition just introduced, rebuild (re-prove) the Prime Minister's contentions and introduce any additional contentions s/he wishes to introduce.
Likewise neighbour discovery via Hello messages can be a source of significant overhead, additional contention and collisions.
Once the channel access has been allocated to the source station, the helper should relay the packet an time after its reception, without any additional channel contention.
Sex education in public schools and legalization of the "morning after pill" have been additional points of contention, with the church opposing both.
Multiple channels of dialogue were established, and both sides sought to use the JCPOA as a foundation from which dialogue on additional points of contention could grow.
There is an additional point of contention in systematic reviews and meta-analysis that is relevant here, namely how much it is acceptable to combine data from similar but not identical interventions, participants, duration, or outcome.
In addition, you should add additional reasoning that support your contentions.
A third of the book is devoted to an ongoing argument between Evans and John Stevens (another prominent steam engineer of the day), much of which had previously appeared in the journal The Medical Repository and to which now Evans added various additional criticisms of Stevens' contentions.
Mr. Friedman began by disagreeing with my contention that additional public investment would yield high returns.
