AS2 Game Script - pushing multiple blocks

I am building a tile based platform style game where the player avatar can push blocks along in order to solve puzzles. All of the normal terrain collision is working fine. The character can also push one block at a time and that pushed block can get terrain collisions just fine.

The problem is in pushing multiple blocks at once. I can’t seem to think of a solution that would allow the character to push a row of blocks and have them accurately check for collisions with the terrain.

I just can’t seem to wrap my head around it. Any suggestions on how I might approach the problem?