YES! You can ALWAYS make a higher offer!
YES! The selling agent is obligated to take ALL WRITTEN offers to the seller,
no matter what: higher, lower, insulting, complimentary, halucinary... by law,
all written offers MUST be presented to the seller.
To make a ridiculous example, if you offered, in writing, to give the seller $1 and punch them in the face, as extreme and insulting as it would be, the agent MUST take this offer to the seller NO MATTER WHAT, all the way until closing and the property is no longer in the seller's possession. I wouldn't recommend such an offer, but I'm just making the point that the agent is obligated to present all written offers.
Inversely, there's no telling what the contract on the property might say and they might not be able to accept your offer, but the agent is bound by law to present it, as long as it's in writing.
The only possible exception to this is if the seller has signed a power of attorney giving the agent authority to act on their behalf and not present offers. Even then, the regular law might take precedence. Of course, I've never heard of such a power of attorney being granted, so it's purely theorhetical and extremely unlikely.