x1 (person(s)) is/are adopted by x2 (individual, family, tribe/clan, community, team, institution, etc.) into the latter's overarching family/clan/tribe/community/team/institution/etc. x4 in(to) role/relation x3 or an analog thereof via means/law/norm/socio-cultural or other mechanism x5; x2 adopts x1 into x2's family11.
x1 is the adoptee; x2 is the adopter. Usually (in modern Western culture), adoption of this type is of a young child (x2) by a soon-to-be parental figure or romantic n-some (x1) into the role of their offspring analog (x3). Note that this definition is in the passive voice in English. The 'step-parent'/'step-child' or even direct spousal or resultant 'in-law' relationships may in some sense be viewed as adoption via marriage. This definition is very broad, but a certain degree of integration is assumed or required (at least for certain purposes). Adoption can be by a community and the 'familial' relationship can be simply a somewhat interpersonally-distant communal one. Adoption need not be by an older or more senior person of a younger or more junior one. x4 is most useful when it differs from x2 (particularly if x2 is an individual). Adoption does not presuppose that no relationship, or even similar relationship, existed prior to the adoption, although it would be odd to adopt someone into exactly the same relationship which they already had attained.