This method has 2 steps, if you don't have the first 2 DLCs skip to 28:40 of the video below.

If you have the DLCs there are a few items that we can get to higher the affinity gained with your friends.

First of all go talk to Argo and buy the "Nostalgic Echo".

Now we have to collect some rare items called Memories, there's 1 for each ally from Arfa-SyS to Rain, unfortunately there's no memory for the DLCs characters; here's a full list of the Memories Locations:

00:46 Arfa-SyS: You need to give her a total Allowance of 100M and she'll give you the Memories as reward

- 02:27 Asuna, Solitary Sands

- 04:06 Leafa, Solitary Sands

- 05:31 Itsuki, Solitary Sands

- 07:15 Zeliska, Solitary Sands, Underground Weapon Plant

- 08:16 Sinon, Solitary Sands, Lighthouse Dephts

- 09:34 Silica, The Old South, Dome

- 11:00 Rain, The Old South, City Ruins East Entrance

- 13:07 Kirito, The Old South, North-East from Subway B

- 15:45 Yuuki, The Old South, Subway A

- 17:40 Argo, The Old South, Abandoned Road Midpoint

- 19:23 Lisbeth, The Old South, Outskirt Facility

- 19:47 Philia,Forgotten Woods, SBC Flügel Gate

- 21:29 Bazalt Joe, Forgotten Woods, Forest Edge Dephts

- 21:59 Strea, Forgotten Woods, SBG Flügel Bow Midpoint

- 25:26 Agil, Forgotten Woods, SBG Flügel Bow Midpoint

- 27:49 Klein, Forgotten Woods, SBC Flügel Dephts

For a detiled walkthrough check the video below: