größtmöglichem
größtmöglichem is the dative singular inflected form of the German adjective größtmöglich, meaning maximal or as large as possible. It appears when the noun it modifies is in the dative case and no determiner is present (strong declension), or after prepositions that require the dative. Examples include mit größtmöglichem Erfolg (with the greatest possible success), in größtmöglichem Maß (in the greatest possible measure), and am größtmöglichen Umfang (at the greatest possible extent). The form is also found in other masculine or neuter dative singular contexts, such as mit größtmöglichem Aufwand or in größtmöglichem Maß.
Größtmöglich is a compound adjective formed from groß (big) and möglich (possible), used to express the upper
Usage of größtmöglichem tends to be formal, technical, or juridical, but it also appears in everyday language
In summary, größtmöglichem is a specific inflected form of größtmöglich used in dative contexts without a determiner