I'm inferring from your question text that

a) you cannot do atomic refresh (ie, delete-insert) because its too expensive/slow, AND

b) you cannot do non-atomic refresh (ie, truncate-insert) because it might break the report

In that case, perhaps you need TWO mviews. The usage would then be:

Initial build
=============
- create mview MV_COPY1
- create mview MV_COPY2
- create or replace synonym MV1 for MV_COPY1

Refesh 1
========
- non-atomic refresh of MV_COPY2
- create or replace synonym MV1 for MV_COPY2

Refesh 2
========
- non-atomic refresh of MV_COPY1
- create or replace synonym MV1 for MV_COPY1

Refesh 3
========
- non-atomic refresh of MV_COPY2
- create or replace synonym MV1 for MV_COPY2


and so on