Why can't I mine in more than one pool at the same time in pool mining?
I thought I could send one share to more than one pool if the difficulty was the same.
It will be possible to increase my reward.
When you mine in a pool, you must try to mine blocks that reward the members of that pool. That's what it means to mine in a pool.
An attempt to mine a block must be an attempt to mine some particular block. If you're attempting to mine a block that pays rewards to the members of pool A, you aren't attempting to mine a block that pays rewards to the members of pool B.
Why can't I mine in more than one pool at the same time in pool mining?
Because no two pools ever try to mine the same block. To mine in a pool, you must be trying to mine the block that pool wishes to mine.
I thought I could send one share to more than one pool if the difficulty was the same.
Nope. If you aren't actually trying to produce the blocks that a pool wants to mine, you are aren't entitled to shares.
It will be possible to increase my reward.
No, it won't. Pool A won't reward you with shares for trying to mine blocks that pay to pool B's members. Why would they? And Pool B will only pay you for trying to mine blocks that pay to their members. Why would they pay you to mine any other blocks?