Increase, enlarge, augment, multiply mean to become or cause to become greater or more numerous.
Increase distinctively carries the idea of progressive growth; sometimes it means nothing more than this. Sometimes it implies growth in numbers by natural propagation or growth in size, amount, or quantity (as by increments or accretions) or growth in intensity, especially by degrees or in proportion to something else.
In transitive use increase may or may not imply progressive growth; often it so stresses the operation or the effectiveness of a cause that it loses the connotation of natural or regular progression.
Enlarge stresses expansion or extension so that whatever is affected is greater in some or all of its dimensions or in its size or capacity.
In extended use enlarge is applicable primarily to what may be thought of as capable of being made larger or smaller in extent or size; thus, one does not enlarge one’s interests or one’s activities but the field of one’s interests, or the scope of one’s activities.
Nevertheless field, scope, or capacity may be merely implied.
Augment, like increase, basically implies growth; it rarely, however, carries the implication of progressive growth or growth by degrees, which is often so strong in increase. It differs from increase chiefly in being used in reference to things already well grown or well developed; thus, when one says “the team’s confidence increases with every victory” one implies that its confidence was originally not strong; on the other hand, when one says “the team’s confidence augments with every victory” one implies that its confidence was never weak. Consequently the distinctive implication of augment is a growing greater, more numerous, larger, or more intense.
Multiply implies an increase in number especially by natural generation. Sometimes, however, the word implies increase in numbers by indefinite repetition of things of the same kind.