Porbably no more than two.

Wait. Do you mean how many offers have you written for one buyer?
Or do you mean how many offers for different buyers?
Back in the day it wasn't that uncommon to write seven or eight offers when inventory was so low and people were writing on multiple properties. Having more than one buyer we are working with write on the same property? I believe the maximum number was 3. That doesn't happen very often these days. Mostly because I do very little residential.

Owner occupied buyers 2. The first home went to a much higher offer. Their second choice of homes they made their best offer first finally listening and it was accepted. For cash investors, just last week i wrote 4 offers for one buyer on 4 different homes

If I recall five was the number...

I believe 2 was the most

For the same buyers, one.

For multiple buyers, two.

Guess I haven't reached peak personal production yet as I've only written 2 in a day so far. Looking forward to challenging myself on this! Thank you Bob and Debe for the motivation! ; )

I believe 1 but maybe 2 Praful Thakkar .

I don't recall but likely more than two.

I go one at a time. 

One.

2 and only bedcuase the first offer got rejected

Two, the original and the highest and best.

I had one day that I wrote four - several months ago but, never more than that.

I wrote 3 just yesterday...none today though!  

Have written four for myself in a day.

I have definitely done 2 maybe 3...

I don't think I have ever written more than 2 offers on the same day...

Three comes to mind! All accepted!

If I had to guess somewhere from 2-4

  3 or 4.   I wish I had that problem more often!

One.

I don't typically write more than one offer per buyer.

I have written three, for three different buyers.

I could tell you about an investor seminar in San Francisco in 2005 but you would think I was making it up on how many we wrote that day. Answer, a lot.

We have had buyers offer on several lots at one time. 

worked them within my first 6 months in the business... quickly became a listing agent.... 

I've had one buyer write on three in a day.

I've had a few out of town buyers that wrote several (3 I think) since they were leaving and we submitted them one after the other until one was accepted

just two.

Just 2. First 1 bust - 2nd one good.

@ Praful Thakkar

When you work with first time buyers who like a tech website like RF, they have one agent showing as many homes while the other agent write endless offers. Since their offers are often lower they write, write, and write offers until one gets notice of a selling agent. Often it takes about 1 dozen offers to get something going.  With experienced agents they tell them upfront the likelihood getting one accepted is slim. How about offer 300K over in better neighborhood and less in so so neighborhood?  No?  Find you another realtor.... Adios. 

During the short sale days- 3 in one day.

Outside of that, never more than one unless they are buying more than one.

This kind of data just does not get rental space in my brain.  If I were to venture a guess, I would say 2-3.  

I do not recall.