I think concentrate on the training contract applications. However, if you finish these in time, by all means apply for more vacation schemes.
I did five vacation schemes in total (Jones Day, Stephenson Harwood, Davies Arnold Cooper, Withers, PricewaterhouseCoopers Legal) and got offered two more (DWF Solicitors and Dawsons), and doing so many didn't prevent me from getting a variety of offers from firms that were ranked above those mentioned here. I didn't always disclose all of them - I tended to select the ones that were more attuned with the firm I was applying to and thus tailored my CV to make my legal experience especially relevant.