Several SD libraries allow multiple open files. The number of files open in SdFat is only limited by SRAM.
You can interleave I/O to open files but performance may suffer since there is only one 512 byte buffer for an SD block.
If you read one byte from the first file then write a byte to a second file 1536 bytes of I/O are required. 512 to read a block from the first file then 512 bytes to read the block from the second file followed by 512 bytes to write the updated block to the second file.
Programs that read and write larger chunks of data work well.
The Arduino SD.h wrapper for SdFat only allows one open file.