se = if purché = as long as, provided that qualora = in case, if a condizione che = on (the) condition that, provided that a patto che = on (the) condition that, provided that nel caso/nel caso che = (just) in case, in the event that casomai (or caso mai) = (just) in case, in the event that
Fabio può ancora collaborare con noi, a patto che si impegni di più. Fabio can still collaborate with us, provided that he works harder.
In the example above, the speaker states that Fabio can still collaborate with them if he applies himself more. If this (hypothetical) situation does not occur, and Fabio does not commit more to the project, it is implied that he will not be allowed to collaborate. A patto che and a condizione che are synonymous.