This is an excerpt from this and this answer of mine. See also this question and answers even though it is about to be marked duplicate.
azair has very powerful search options (see the advanced options), including choice of return and departure day, length of stay, period within which the trip should happen and a range of departure and arrival airports. Exactly as you ask they look for connections on separate tickets (consider also this Q&A), even on different (low-cost) airlines.
Skypicker does the same and let's you circle departure/destination in on a map, has date range and also some kind of "promise" to help you if you miss a non-guaranteed connection.
Finally be aware of pro's and con's of flying on separate tickets.