Naturally, one may always raise rates - even though one risks being replaced or just generally souring the client relationship.
A 60-80% increase could be viewed as extortion by the client unless they acknowledge that your role has changed considerably, e.g. from 'just' producing to architecting solutions and/or managing others.
The only time I succeeded raising my rate during a contract, it was by 33% in a situation where I had accepted a low rate because of financial necessity - so the increase merely brought me up to current market rates. I illustrated this by interviewing at potential future clients, which made the current client accept the increase.
Clients are capitalists; they have a lot more respect for what the market values you at, than your own (more vague) claims. Generally, making them pay a fair market rate doesn't seem to affect the relationship, whereas 'forcing' them to comply with what they feel is a unjustified increase, very probably will have a negative impact sooner or later.