My view:
1) If you are affected by a redundant condition, this does not result in you needing to make multiple saves to get out of it. Similarly, if one condition overrides another (10 poison damage replacing 5 poison damage), only the bigger effect is still in play.
2) If you are affected by two highly-similar conditions, even the tiniest game-relevant difference is enough to requier seperate saves.
Examples:
Example 1) You are suffering from 10 Ongoing Fire Damage (save ends). An enemy hits with an attack that deals 5 Ongoing Fire Damage (save ends). These do not stack, and you make a single save against ongoing fire damage each round - once it is made, you are no longer taking ongoing fire damage.
Example 2) You are suffering from 10 Ongoing Fire Damage (save ends). An enemy hits with an attack that deals 5 Ongoing Fire Damage and Dazes (save ends both). The ongoing fire damage does not stack, but you are still suffering from both conditions, and each round both take 10 fire damage and are dazed. Each round, you save once against the 10 ongoing fire damage, and once against the 5 ongoing fire damage + daze. If you save against the 10 ongoing fire damage, you are now dealing with the full effect of the second ability, and taking 5 ongoing fire damage and dazed until you save against that effect.