Yes definitely! All the private colleges which take admission through UPSEE also take admission through the spot counselling round. Some of the top private colleges in which you can take admission through the spot counselling of UPSEE are as follows:

Integral University, Lucknow

IET Lucknow - Institute of Engineering and Technology

AKGEC Ghaziabad - Ajay Kumar Garg Engineering College

GL Bajaj Institute of Technology and Management, Greater Noida

Galgotias University, Greater Noida

ABES Engineering College, Ghaziabad

Hope I have answered your question. All the best!