Following a request, here is a list of all the games to date where there has been an offer made at a non-standard stage of the game. I don't intend to keep on updating this list, so make the most of it while it's current.

Offers after every box in the final round, not as part of any specific theme

Ned - 4-12-2006 - game 320
Wrighty - 25-12-2006 - game 339
Danny - 26-12-2006 - game 341
Annie - 29-6-2007 - game 500
Hayley - 31-12-2007 - game 633
Mark - 21-3-2008 - game 703
Chris - 15-7-2008 - game 802

Offers after every box in the final round, Trick or Treat twist

Ben - 29-10-2007 - game 579
Tina - 30-10-2007 - game 580
Chris - 31-10-2007 - game 581
Little Rich - 1-11-2007 - game 582
Maria - 2-11-2007 - game 583
Whitey - 27-10-2008 - game 866
Pammy - 28-10-2008 - game 867
Tony - 29-10-2008 - game 868
Karina - 31-10-2008 - game 870
Pam - 2-11-2008 - game 871

Offers after every box in the final round, Scrooge or Santa twist

Patricia - 20-12-2007 - game 624
Orry - 21-12-2007 - game 625
Stephen - 22-12-2007 - game 626
Sam - 15-12-2008 - game 908
Stan - 19-12-2008 - game 912
Lauren - 20-12-2008 - game 913
Billy - 21-12-2008 - game 914
Jane - 22-12-2008 - game 915

Offers after every box in the final round, Banker's Birthday twist

Tom - 12-5-2008 - game 747
Mark - 12-5-2008 - game 750

Offers after every box in the final round, Summer Special twist

Derek - 21-7-2008 - game 807
Helen - 24-7-2008 - game 810

Valentine's/Love Week twist

Viv - 11-2-2008 - game 669 - offer made at 4-box stage
Richie - 12-2-2008 - game 670 - offer made at 6-box stage
Rachel - 13-2-2008 - game 671 - offer made at 3-box stage
Bing - 14-2-2008 - game 672 - offer made at 3-box stage
Chris - 15-2-2008 - game 673 - offer made at 3-box stage
Alfonso - 9-2-2009 - game 956 - offer made at 7-box stage
Ash - 10-2-2009 - game 957 - offer made at 6-box stage
Clare-Louise - 11-2-2009 - game 958 - offer made at 7-box stage
Del - 12-2-2009 - game 959 - offer made at 4-box stage
Melissa - 13-2-2009 - game 960 - offer made at 4-box stage
Sue - 15-2-2009 - game 961 - offer made at 4-box stage

Other one-offs

Rich - 27-3-2007 - game 419 - offer made at 10-box stage
Carla - 16-2-2009 - game 962 - offer made at 7-box stage
Natalie - 8-4-2009 - game 1006 - offer made at 6-box stage

That's quite interesting. Thank you for posting this, MisterAl.

I was interested in seeing Rich's game (27-3-2007) with a 10-box offer, so had a look at the game again.

Now I'm intrigued when we'll see a 9-box offer...

Vera could now be on the one-off list too.

Oh and Ollie of course!!

By my reckoning, in addition to Ollie and Vera, there's another 7 who could be added to the list - Danielle (as an "other one-off") and of course Kris, Shell, Nicola, Scarlet, Pezza and Liam as part of the banker's birthday specials.

Declan!