These are the results for the stressnet:

https://www.reddit.com/r/Monero/comments/1eoana8/the_stressnet_so_far/

TL;DR:

*Most transactions in a block is 4909 at height 2535307

*Most transactions cleared in 30 consecutive blocks: 100863 transactions starting at block 2547555.

So the maximum TX/day the Monero network could handle seems to be somewhere between 2.4 million and 3.5 million. That would be a max TPS of ~41.

For current TX/day look at this site for example:

https://bitinfocharts.com/de/comparison/monero-transactions.html

So it looks like we actually have a headroom of about 130x when it comes to TX throughput.

Though the number for the actual mainnet is probably a little lower than for the stressnet I'd guess.