No need to go wider, just use much better tires than that shit Silverstone! My recommendation to you are listed below in order:
Michelin PS3: the best, most well balanced high performance tire for this size. Also the most expensive (close to rm250/pc) but worth it!
Goodyear F1D5: practically match PS3 very close, also excellent well balanced tire between dry & wet performance with pretty good durability too. Price also almost reaching PS3, maybe just a bit cheaper.
Hankook V12 Evo2: so far today  should be the best value for money as it's the cheapest in this list (only around rm180/pc) but gives performance almost as good.
Bridgestone RE003: excellent in the dry (maybe the best) but not as good in the wet, seems to focus more on dry performance than the rest in this list. Also will finish off the soonest coz the tread wear is the lowest at only 220 (the rest are 300 or above so last longer). Price now maybe around rm200-220/pc.
Yokohama Advan Fleva V701: the newest tire in this list but seems also the one with the most mixed reviews, some say decent enough but some say not so good too. Price similar to RE003.