。
Their communication may be far more complex than we have thought.
Literal
Their communication [topic-は] we [subject-が] thought-come thing [comparative-より] by-far complex [might-かもしれません].
A comparative structure with nested clauses. The pattern [X]より[Y] ('more Y than X') takes a full clause as X: 我々が考えてきたもの = 'the thing (we) have been thinking.' Inside that clause, 考えてきた uses ~てくる to express an action continued up to the present ('have been X-ing'). はるかに ('far, by far') intensifies 複雑. The final かもしれません hedges the whole claim.