Ran on most recent partition:

ALTER TABLE xxxx REBUILD PARTITION = 165 WITH (DATA_COMPRESSION = PAGE)

The next partition via split function was also compressed at page level. Only had to run ALTER TABLE to begin the cycle of compression on new partitions. Sliding window partitioning strategy.

165 days from now, when these new partitions are ready to be switched out, the switch-in table has to be compressed, if I don't rebuild all partitions before then and make adjustments to the switch-in table at time when all partitions are compressed.

So it is true, mixed compressed partitions can co-exist with partitioned table.

If you have a lot of partitions and oldest are not used very much or an entire partitoned table isn't used much, can compressed most unused partitions to save space. CPU will be used more to unpack so if CPU has little further capacity, forget it.