The name of student council president is Sarashiki Tatenashi.
Tatenashi is not a name usually given to a girl. It seems the name 'Tatenashi' is a title given to the current head of Sarashiki family, and she is the 17th holder since the foundation of the family.
The Sarashiki family is actually an underground peacekeeping organization that thwarts secret, evil plots of other secret (and probably evil) organizations which tries to adversely influence the world.
Although I would love to see Tatenashi becoming a member of Ichika's harem, I think it is highly unlikely.
The reason is simple... she is way too strong to maintain any kind of balance among previous heroines.
Let's face it.
She is much stronger than Laura in hand-to-hand / IS battle.
She is at least as much attractive (visually) as Houki.
She is as much influential as Cecilia is.
She is as much sociable as Charlotte is.
She appears as much open to Ichika as Rin is. (in terms of skin-ship).
Each of those is the prominent strong point of the 5 heroines.
On top of that, she doesn't seem to have any of the weakness so far.
Sure, it's possible that she may turn out to be even worse cook than Cecilia (Currently the worst among 5 heroines), but that's not even close to being handicap enough to offset her numerous strong points.
BTW, the cooking skills (and ranking) of 5 heroines are...
======= Safe Zone =================
1st - Houki/Charlotte - Looks great & delicious
3rd - Rin - Looks weird but delicious
(Except for Chinese food in which she is on par with Houki)
======= Danger Zone =================
4th - Laura - Looks weird but somehow edible.
======= Kill Zone =================
5th - Cecilia - Looks exactly same as the picture from cookbook, but tastes like cookbook too.
===============================
※Ichika's position (Looks good, tastes good) would probably be slightly above Rin.
Personally, I can't think of a situation with Tatenashi in distress, asking for, or requiring Ichika's help.
Also, she doesn't seem to actually love him. It's more like she treats him as an 'interesting subject' and nothing more.
Yes, she temporarily moves into Ichika's room, but it's because she is protecting him from an unknown (therefore probably evil) organization which tries to steal Ichika's IS (and also attack him directly)
She acts as his bodyguards by sharing the same room and also trains him to be stronger so he could better protect himself - all the while flirting with him which angers other heroines greatly.
As for Ichika.... I don't know how he is going to be stronger any more.
His IS is already in 2nd Form, and he already has One Off.
(The ISs of other heroines are in 1st Form, and except for Houki, they still don't have One Off)
Since accumulation of experience between pilot and IS plays a large role, so 'switching to much stronger IS' plot seems highly unlikely.
So it's either his IS somehow become stronger (sprouts multi-core capability perhaps, and gains a second One Off, maybe?), or Ichika himself turns out to be something special, other than 'being the only male in the world to pilot IS' stuff which, while being a great advertisement, does not actually help much in battle.
P.S.
Still, it's still possible that Tatenashi ends up becoming a member of Ichika's harem, but it would require re-balancing of at least 6 people(the heroines and Tatenashi)
It's either Ichika and his girls become much stronger or Tatenashi becomes weaker...
Fortunately, the girls could power-up sufficiently by attaining 2nd Form and One Off
They could also count on their countries for additional support.
(Houki can neither attain One Off(she already has one) nor count on support from major organization, but since she has the 'God of IS tech' as her personal support, it wouldn't be a problem)
※ Since Ichika is also one of 3 people Tanabe cares, he could also benefit from her support.
The current IS battle ranking among IS Academy freshman is...
1st - Laura
2nd - Charlotte
3rd - Rin
4th - Houki
5th - Ichika
6th - Cecilia
Laura is very skilled pilot, and she has experience in IS operation due to her military background.
Charlotte is about equally skilled although she is not as much experienced as Laura.
Rin is also a very skilled pilot. Considering the fact that she has the shortest training background among 5 heroines, she is not only talented but also a hard worker.
Houki is not as skilled as others, (she got C for aptitude test, while most rep. candidates usually get an A or S) and she often lose her cool-headedness during the combat, but these are somewhat offset by her powerful IS (fielding the latest technologies) which is personally designed by Tabane to maximize her strength.
Cecilia is currently (at the time of novel Vol.5) suffering the most since she is not yet able to utilize the BT system to proficient level. Also, her IS is armed mostly with energy-based weapon, which makes her IS ill-matched for Ichika's Byakku Shiki, which can negate energy-based attack with its shield.