In principle, "in furtherance of this agreement" doesn't have precisely the same meaning as "on the basis of this agreement". "On the basis of", to my mind, means the same as "under (the terms of)", "pursuant to", "by virtue of". All these refer to things that the terms of the agreement require or allow to be done. "In furtherance of", properly used, should refer to something done to advance the aims for which the agreement was entered into. Of course there is a considerable overlap, and things done under the terms of the agreement are likely to be in furtherance of it, and vice versa, but the perspective is strictly distinct. In particular cases, however, the person who drafted the contract may not actually be making that distinction and may in practice be treating "in furtherance of" as a synonym of "on the basis of". Many people, including translators, fail to observe fine distinctions of this kind.

Consider the following example, from the Irish Construction Contracts Act 2013:

"“work”, in relation to a construction contract, means any act done in furtherance of the construction contract under the terms of the construction contract."
http://www.irishstatutebook.ie/eli/2013/act/34/section/1/ena...

Note how "in furtherance of" is here distinguished from "under the terms of". The latter means that the terms of the contract require or allow the work to be done; the former means that the work contributes to implementing and realising the purposes of the agreement: the purpose of the agreement is to carry out a construction and the work contributes to that end.

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Note added at 1 day 2 hrs (2017-12-25 16:12:04 GMT) Post-grading
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And Veselé Vánoce to you, Pavel :-)