I have a building with two networks ... a clientside and office side.   The client side consist of a router and 7 switches ( all TL-SG1218MPE), one per floor.   The office side consist of a router and 1 switch ( TL-SG2428P v5.0) .... The 2 routers get internet via a ISP modem/ router. 

The switches on the client side are linked to each other via ports 17 and 18  ----       router > port 18 /switch 1 / port 17 > port 18 / switch 2/ port 17 > so on to 7th switch

The problem is we have an office on the 3rd floor of the client side that I would like to have on the office network. 

Is it possible, via vlan config to have the switches carry office traffic (10.x.x.x)  on the switches on the client side (192.x.x.x) ....   

my thought is to create a vlan for 10.1.x.x traffic on switch 1 which is in the network room with the routers then configure the switch on 3rd floor to assign the vlan to a port that can be used to "power" the network jack in the 3rd floor office

is my theory doable? if so how would the config look? Do the other switches need to be config a certain way?